ВычМат лабы 2 курс 1 сем / CM_21_11 / Практическая работа №11 Решение системы линейных уравнений [se.moevm.info]

Практическая работа №11: Решение системы линейных уравнений [se.moevm.info] (function(H){H.className=H.className.replace(/\bno-js\b/,'js')})(document.documentElement) /**/ .iris-picker{display:block;position:relative}.iris-picker,.iris-picker *{-moz-box-sizing:content-box;-webkit-box-sizing:content-box;box-sizing:content-box}input+.iris-picker{margin-top:4px}.iris-error{background-color:#ffafaf}.iris-border{border-radius:3px;border:1px solid #aaa;width:200px;background-color:#fff}.iris-picker-inner{position:absolute;top:0;right:0;left:0;bottom:0}.iris-border .iris-picker-inner{top:10px;right:10px;left:10px;bottom:10px}.iris-picker .iris-square-inner{position:absolute;left:0;right:0;top:0;bottom:0}.iris-picker .iris-square,.iris-picker .iris-slider,.iris-picker .iris-square-inner,.iris-picker .iris-palette{border-radius:3px;box-shadow:inset 0 0 5px rgba(0,0,0,.4);height:100%;width:12.5%;float:left;margin-right:5%}.iris-picker .iris-square{width:76%;margin-right:10%;position:relative}.iris-picker .iris-square-inner{width:auto;margin:0}.iris-ie-9 .iris-square,.iris-ie-9 .iris-slider,.iris-ie-9 .iris-square-inner,.iris-ie-9 .iris-palette{box-shadow:none;border-radius:0}.iris-ie-9 .iris-square,.iris-ie-9 .iris-slider,.iris-ie-9 .iris-palette{outline:1px solid rgba(0,0,0,.1)}.iris-ie-lt9 .iris-square,.iris-ie-lt9 .iris-slider,.iris-ie-lt9 .iris-square-inner,.iris-ie-lt9 .iris-palette{outline:1px solid #aaa}.iris-ie-lt9 .iris-square .ui-slider-handle{outline:1px solid #aaa;background-color:#fff;-ms-filter:"alpha(Opacity=30)"}.iris-ie-lt9 .iris-square .iris-square-handle{background:0;border:3px solid #fff;-ms-filter:"alpha(Opacity=50)"}.iris-picker .iris-strip{margin-right:0;position:relative}.iris-picker .iris-strip .ui-slider-handle{position:absolute;background:0;margin:0;right:-3px;left:-3px;border:4px solid #aaa;border-width:4px 3px;width:auto;height:6px;border-radius:4px;box-shadow:0 1px 2px rgba(0,0,0,.2);opacity:.9;z-index:5;cursor:ns-resize}.iris-strip .ui-slider-handle:before{content:" ";position:absolute;left:-2px;right:-2px;top:-3px;bottom:-3px;border:2px solid #fff;border-radius:3px}.iris-picker .iris-slider-offset{position:absolute;top:11px;left:0;right:0;bottom:-3px;width:auto;height:auto;background:transparent;border:0;border-radius:0}.iris-picker .iris-square-handle{background:transparent;border:5px solid #aaa;border-radius:50%;border-color:rgba(128,128,128,.5);box-shadow:none;width:12px;height:12px;position:absolute;left:-10px;top:-10px;cursor:move;opacity:1;z-index:10}.iris-picker .ui-state-focus .iris-square-handle{opacity:.8}.iris-picker .iris-square-handle:hover{border-color:#999}.iris-picker .iris-square-value:focus .iris-square-handle{box-shadow:0 0 2px rgba(0,0,0,.75);opacity:.8}.iris-picker .iris-square-handle:hover::after{border-color:#fff}.iris-picker .iris-square-handle::after{position:absolute;bottom:-4px;right:-4px;left:-4px;top:-4px;border:3px solid #f9f9f9;border-color:rgba(255,255,255,.8);border-radius:50%;content:" "}.iris-picker .iris-square-value{width:8px;height:8px;position:absolute}.iris-ie-lt9 .iris-square-value,.iris-mozilla .iris-square-value{width:1px;height:1px}.iris-palette-container{position:absolute;bottom:0;left:0;margin:0;padding:0}.iris-border .iris-palette-container{left:10px;bottom:10px}.iris-picker .iris-palette{margin:0;cursor:pointer}.iris-square-handle,.ui-slider-handle{border:0;outline:0} /**/ .MathJax_Hover_Frame {border-radius: .25em; -webkit-border-radius: .25em; -moz-border-radius: .25em; -khtml-border-radius: .25em; box-shadow: 0px 0px 15px #83A; -webkit-box-shadow: 0px 0px 15px #83A; -moz-box-shadow: 0px 0px 15px #83A; -khtml-box-shadow: 0px 0px 15px #83A; border: 1px solid #A6D ! important; display: inline-block; position: absolute} .MathJax_Menu_Button .MathJax_Hover_Arrow {position: absolute; cursor: pointer; display: inline-block; border: 2px solid #AAA; border-radius: 4px; -webkit-border-radius: 4px; -moz-border-radius: 4px; -khtml-border-radius: 4px; font-family: 'Courier New',Courier; font-size: 9px; color: #F0F0F0} .MathJax_Menu_Button .MathJax_Hover_Arrow span {display: block; background-color: #AAA; border: 1px solid; border-radius: 3px; line-height: 0; padding: 4px} .MathJax_Hover_Arrow:hover {color: white!important; border: 2px solid #CCC!important} .MathJax_Hover_Arrow:hover span {background-color: #CCC!important} #MathJax_About {position: fixed; left: 50%; width: auto; text-align: center; border: 3px outset; padding: 1em 2em; background-color: #DDDDDD; color: black; cursor: default; font-family: message-box; font-size: 120%; font-style: normal; text-indent: 0; text-transform: none; line-height: normal; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; z-index: 201; border-radius: 15px; -webkit-border-radius: 15px; -moz-border-radius: 15px; -khtml-border-radius: 15px; box-shadow: 0px 10px 20px #808080; -webkit-box-shadow: 0px 10px 20px #808080; -moz-box-shadow: 0px 10px 20px #808080; -khtml-box-shadow: 0px 10px 20px #808080; filter: progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')} #MathJax_About.MathJax_MousePost {outline: none} .MathJax_Menu {position: absolute; background-color: white; color: black; width: auto; padding: 2px; border: 1px solid #CCCCCC; margin: 0; cursor: default; font: menu; text-align: left; text-indent: 0; text-transform: none; line-height: normal; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; z-index: 201; box-shadow: 0px 10px 20px #808080; -webkit-box-shadow: 0px 10px 20px #808080; -moz-box-shadow: 0px 10px 20px #808080; -khtml-box-shadow: 0px 10px 20px #808080; filter: progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')} .MathJax_MenuItem {padding: 2px 2em; background: transparent} .MathJax_MenuArrow {position: absolute; right: .5em; padding-top: .25em; color: #666666; font-size: .75em} .MathJax_MenuActive .MathJax_MenuArrow {color: white} .MathJax_MenuArrow.RTL {left: .5em; right: auto} .MathJax_MenuCheck {position: absolute; left: .7em} .MathJax_MenuCheck.RTL {right: .7em; left: auto} .MathJax_MenuRadioCheck {position: absolute; left: 1em} .MathJax_MenuRadioCheck.RTL {right: 1em; left: auto} .MathJax_MenuLabel {padding: 2px 2em 4px 1.33em; font-style: italic} .MathJax_MenuRule {border-top: 1px solid #CCCCCC; margin: 4px 1px 0px} .MathJax_MenuDisabled {color: GrayText} .MathJax_MenuActive {background-color: Highlight; color: HighlightText} .MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus {background-color: #E8E8E8} .MathJax_ContextMenu:focus {outline: none} .MathJax_ContextMenu .MathJax_MenuItem:focus {outline: none} #MathJax_AboutClose {top: .2em; right: .2em} .MathJax_Menu .MathJax_MenuClose {top: -10px; left: -10px} .MathJax_MenuClose {position: absolute; cursor: pointer; display: inline-block; border: 2px solid #AAA; border-radius: 18px; -webkit-border-radius: 18px; -moz-border-radius: 18px; -khtml-border-radius: 18px; font-family: 'Courier New',Courier; font-size: 24px; color: #F0F0F0} .MathJax_MenuClose span {display: block; background-color: #AAA; border: 1.5px solid; border-radius: 18px; -webkit-border-radius: 18px; -moz-border-radius: 18px; -khtml-border-radius: 18px; line-height: 0; padding: 8px 0 6px} .MathJax_MenuClose:hover {color: white!important; border: 2px solid #CCC!important} .MathJax_MenuClose:hover span {background-color: #CCC!important} .MathJax_MenuClose:hover:focus {outline: none} .MathJax_Preview .MJXf-math {color: inherit!important} .MJX_Assistive_MathML {position: absolute!important; top: 0; left: 0; clip: rect(1px, 1px, 1px, 1px); padding: 1px 0 0 0!important; border: 0!important; height: 1px!important; width: 1px!important; overflow: hidden!important; display: block!important; -webkit-touch-callout: none; -webkit-user-select: none; -khtml-user-select: none; -moz-user-select: none; -ms-user-select: none; user-select: none} .MJX_Assistive_MathML.MJX_Assistive_MathML_Block {width: 100%!important} #MathJax_Zoom {position: absolute; background-color: #F0F0F0; overflow: auto; display: block; z-index: 301; padding: .5em; border: 1px solid black; margin: 0; font-weight: normal; font-style: normal; text-align: left; text-indent: 0; text-transform: none; line-height: normal; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; -webkit-box-sizing: content-box; -moz-box-sizing: content-box; box-sizing: content-box; box-shadow: 5px 5px 15px #AAAAAA; -webkit-box-shadow: 5px 5px 15px #AAAAAA; -moz-box-shadow: 5px 5px 15px #AAAAAA; -khtml-box-shadow: 5px 5px 15px #AAAAAA; filter: progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')} #MathJax_ZoomOverlay {position: absolute; left: 0; top: 0; z-index: 300; display: inline-block; width: 100%; height: 100%; border: 0; padding: 0; margin: 0; background-color: white; opacity: 0; filter: alpha(opacity=0)} #MathJax_ZoomFrame {position: relative; display: inline-block; height: 0; width: 0} #MathJax_ZoomEventTrap {position: absolute; left: 0; top: 0; z-index: 302; display: inline-block; border: 0; padding: 0; margin: 0; background-color: white; opacity: 0; filter: alpha(opacity=0)} .MathJax_Preview {color: #888} #MathJax_Message {position: fixed; left: 1px; bottom: 2px; background-color: #E6E6E6; border: 1px solid #959595; margin: 0px; padding: 2px 8px; z-index: 102; color: black; font-size: 80%; width: auto; white-space: nowrap} #MathJax_MSIE_Frame {position: absolute; top: 0; left: 0; width: 0px; z-index: 101; border: 0px; margin: 0px; padding: 0px} .MathJax_Error {color: #CC0000; font-style: italic} .MJXp-script {font-size: .8em} .MJXp-right {-webkit-transform-origin: right; -moz-transform-origin: right; -ms-transform-origin: right; -o-transform-origin: right; transform-origin: right} .MJXp-bold {font-weight: bold} .MJXp-italic {font-style: italic} .MJXp-scr {font-family: MathJax_Script,'Times New Roman',Times,STIXGeneral,serif} .MJXp-frak {font-family: MathJax_Fraktur,'Times New Roman',Times,STIXGeneral,serif} .MJXp-sf {font-family: MathJax_SansSerif,'Times New Roman',Times,STIXGeneral,serif} .MJXp-cal {font-family: MathJax_Caligraphic,'Times New Roman',Times,STIXGeneral,serif} .MJXp-mono {font-family: MathJax_Typewriter,'Times New Roman',Times,STIXGeneral,serif} .MJXp-largeop {font-size: 150%} .MJXp-largeop.MJXp-int {vertical-align: -.2em} .MJXp-math {display: inline-block; line-height: 1.2; text-indent: 0; font-family: 'Times New Roman',Times,STIXGeneral,serif; white-space: nowrap; border-collapse: collapse} .MJXp-display {display: block; text-align: center; margin: 1em 0} .MJXp-math span {display: inline-block} .MJXp-box {display: block!important; text-align: center} .MJXp-box:after {content: " "} .MJXp-rule {display: block!important; margin-top: .1em} .MJXp-char {display: block!important} .MJXp-mo {margin: 0 .15em} .MJXp-mfrac {margin: 0 .125em; vertical-align: .25em} .MJXp-denom {display: inline-table!important; width: 100%} .MJXp-denom > * {display: table-row!important} .MJXp-surd {vertical-align: top} .MJXp-surd > * {display: block!important} .MJXp-script-box > * {display: table!important; height: 50%} .MJXp-script-box > * > * {display: table-cell!important; vertical-align: top} .MJXp-script-box > *:last-child > * {vertical-align: bottom} .MJXp-script-box > * > * > * {display: block!important} .MJXp-mphantom {visibility: hidden} .MJXp-munderover {display: inline-table!important} .MJXp-over {display: inline-block!important; text-align: center} .MJXp-over > * {display: block!important} .MJXp-munderover > * {display: table-row!important} .MJXp-mtable {vertical-align: .25em; margin: 0 .125em} .MJXp-mtable > * {display: inline-table!important; vertical-align: middle} .MJXp-mtr {display: table-row!important} .MJXp-mtd {display: table-cell!important; text-align: center; padding: .5em 0 0 .5em} .MJXp-mtr > .MJXp-mtd:first-child {padding-left: 0} .MJXp-mtr:first-child > .MJXp-mtd {padding-top: 0} .MJXp-mlabeledtr {display: table-row!important} .MJXp-mlabeledtr > .MJXp-mtd:first-child {padding-left: 0} .MJXp-mlabeledtr:first-child > .MJXp-mtd {padding-top: 0} .MJXp-merror {background-color: #FFFF88; color: #CC0000; border: 1px solid #CC0000; padding: 1px 3px; font-style: normal; font-size: 90%} .MJXp-scale0 {-webkit-transform: scaleX(.0); -moz-transform: scaleX(.0); -ms-transform: scaleX(.0); -o-transform: scaleX(.0); transform: scaleX(.0)} .MJXp-scale1 {-webkit-transform: scaleX(.1); -moz-transform: scaleX(.1); -ms-transform: scaleX(.1); -o-transform: scaleX(.1); transform: scaleX(.1)} .MJXp-scale2 {-webkit-transform: scaleX(.2); -moz-transform: scaleX(.2); -ms-transform: scaleX(.2); -o-transform: scaleX(.2); transform: scaleX(.2)} .MJXp-scale3 {-webkit-transform: scaleX(.3); -moz-transform: scaleX(.3); -ms-transform: scaleX(.3); -o-transform: scaleX(.3); transform: scaleX(.3)} .MJXp-scale4 {-webkit-transform: scaleX(.4); -moz-transform: scaleX(.4); -ms-transform: scaleX(.4); -o-transform: scaleX(.4); transform: scaleX(.4)} .MJXp-scale5 {-webkit-transform: scaleX(.5); -moz-transform: scaleX(.5); -ms-transform: scaleX(.5); -o-transform: scaleX(.5); transform: scaleX(.5)} .MJXp-scale6 {-webkit-transform: scaleX(.6); -moz-transform: scaleX(.6); -ms-transform: scaleX(.6); -o-transform: scaleX(.6); transform: scaleX(.6)} .MJXp-scale7 {-webkit-transform: scaleX(.7); -moz-transform: scaleX(.7); -ms-transform: scaleX(.7); -o-transform: scaleX(.7); transform: scaleX(.7)} .MJXp-scale8 {-webkit-transform: scaleX(.8); -moz-transform: scaleX(.8); -ms-transform: scaleX(.8); -o-transform: scaleX(.8); transform: scaleX(.8)} .MJXp-scale9 {-webkit-transform: scaleX(.9); -moz-transform: scaleX(.9); -ms-transform: scaleX(.9); -o-transform: scaleX(.9); transform: scaleX(.9)} .MathJax_PHTML .noError {vertical-align: ; font-size: 90%; text-align: left; color: black; padding: 1px 3px; border: 1px solid} .mjx-chtml {display: inline-block; line-height: 0; text-indent: 0; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 100%; font-size-adjust: none; letter-spacing: normal; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0; min-height: 0; border: 0; margin: 0; padding: 1px 0} .MJXc-display {display: block; text-align: center; margin: 1em 0; padding: 0} .mjx-chtml[tabindex]:focus, body :focus .mjx-chtml[tabindex] {display: inline-table} .mjx-full-width {text-align: center; display: table-cell!important; width: 10000em} .mjx-math {display: inline-block; border-collapse: separate; border-spacing: 0} .mjx-math * {display: inline-block; -webkit-box-sizing: content-box!important; -moz-box-sizing: content-box!important; box-sizing: content-box!important; text-align: left} .mjx-numerator {display: block; text-align: center} .mjx-denominator {display: block; text-align: center} .MJXc-stacked {height: 0; position: relative} .MJXc-stacked > * {position: absolute} .MJXc-bevelled > * {display: inline-block} .mjx-stack {display: inline-block} .mjx-op {display: block} .mjx-under {display: table-cell} .mjx-over {display: block} .mjx-over > * {padding-left: 0px!important; padding-right: 0px!important} .mjx-under > * {padding-left: 0px!important; padding-right: 0px!important} .mjx-stack > .mjx-sup {display: block} .mjx-stack > .mjx-sub {display: block} .mjx-prestack > .mjx-presup {display: block} .mjx-prestack > .mjx-presub {display: block} .mjx-delim-h > .mjx-char {display: inline-block} .mjx-surd {vertical-align: top} .mjx-mphantom * {visibility: hidden} .mjx-merror {background-color: #FFFF88; color: #CC0000; border: 1px solid #CC0000; padding: 2px 3px; font-style: normal; font-size: 90%} .mjx-annotation-xml {line-height: normal} .mjx-menclose > svg {fill: none; stroke: currentColor} .mjx-mtr {display: table-row} .mjx-mlabeledtr {display: table-row} .mjx-mtd {display: table-cell; text-align: center} .mjx-label {display: table-row} .mjx-box {display: inline-block} .mjx-block {display: block} .mjx-span {display: inline} .mjx-char {display: block; white-space: pre} .mjx-itable {display: inline-table; width: auto} .mjx-row {display: table-row} .mjx-cell {display: table-cell} .mjx-table {display: table; width: 100%} .mjx-line {display: block; height: 0} .mjx-strut {width: 0; padding-top: 1em} .mjx-vsize {width: 0} .MJXc-space1 {margin-left: .167em} .MJXc-space2 {margin-left: .222em} .MJXc-space3 {margin-left: .278em} .mjx-chartest {display: block; visibility: hidden; position: absolute; top: 0; line-height: normal; font-size: 500%} .mjx-chartest .mjx-char {display: inline} .mjx-chartest .mjx-box {padding-top: 1000px} .MJXc-processing {visibility: hidden; position: fixed; width: 0; height: 0; overflow: hidden} .MJXc-processed {display: none} .mjx-test {display: block; font-style: normal; font-weight: normal; font-size: 100%; font-size-adjust: none; text-indent: 0; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow: hidden; height: 1px} .mjx-ex-box-test {position: absolute; width: 1px; height: 60ex} .mjx-line-box-test {display: table!important} .mjx-line-box-test span {display: table-cell!important; width: 10000em!important; min-width: 0; max-width: none; padding: 0; border: 0; margin: 0} #MathJax_CHTML_Tooltip {background-color: InfoBackground; color: InfoText; border: 1px solid black; box-shadow: 2px 2px 5px #AAAAAA; -webkit-box-shadow: 2px 2px 5px #AAAAAA; -moz-box-shadow: 2px 2px 5px #AAAAAA; -khtml-box-shadow: 2px 2px 5px #AAAAAA; padding: 3px 4px; z-index: 401; position: absolute; left: 0; top: 0; width: auto; height: auto; display: none} .mjx-chtml .mjx-noError {line-height: 1.2; vertical-align: ; font-size: 90%; text-align: left; color: black; padding: 1px 3px; border: 1px solid} .MJXc-TeX-unknown-R {font-family: STIXGeneral,'Cambria Math','Arial Unicode MS',serif; font-style: normal; font-weight: normal} .MJXc-TeX-unknown-I {font-family: STIXGeneral,'Cambria Math','Arial Unicode MS',serif; font-style: italic; font-weight: normal} .MJXc-TeX-unknown-B {font-family: STIXGeneral,'Cambria Math','Arial Unicode MS',serif; font-style: normal; font-weight: bold} .MJXc-TeX-unknown-BI {font-family: STIXGeneral,'Cambria Math','Arial Unicode MS',serif; font-style: italic; font-weight: bold} .MJXc-TeX-ams-R {font-family: MJXc-TeX-ams-R,MJXc-TeX-ams-Rw} .MJXc-TeX-cal-B {font-family: MJXc-TeX-cal-B,MJXc-TeX-cal-Bx,MJXc-TeX-cal-Bw} .MJXc-TeX-frak-R {font-family: MJXc-TeX-frak-R,MJXc-TeX-frak-Rw} .MJXc-TeX-frak-B {font-family: MJXc-TeX-frak-B,MJXc-TeX-frak-Bx,MJXc-TeX-frak-Bw} .MJXc-TeX-math-BI {font-family: MJXc-TeX-math-BI,MJXc-TeX-math-BIx,MJXc-TeX-math-BIw} .MJXc-TeX-sans-R {font-family: MJXc-TeX-sans-R,MJXc-TeX-sans-Rw} .MJXc-TeX-sans-B {font-family: MJXc-TeX-sans-B,MJXc-TeX-sans-Bx,MJXc-TeX-sans-Bw} .MJXc-TeX-sans-I {font-family: MJXc-TeX-sans-I,MJXc-TeX-sans-Ix,MJXc-TeX-sans-Iw} .MJXc-TeX-script-R {font-family: MJXc-TeX-script-R,MJXc-TeX-script-Rw} .MJXc-TeX-type-R {font-family: MJXc-TeX-type-R,MJXc-TeX-type-Rw} .MJXc-TeX-cal-R {font-family: MJXc-TeX-cal-R,MJXc-TeX-cal-Rw} .MJXc-TeX-main-B {font-family: MJXc-TeX-main-B,MJXc-TeX-main-Bx,MJXc-TeX-main-Bw} .MJXc-TeX-main-I {font-family: MJXc-TeX-main-I,MJXc-TeX-main-Ix,MJXc-TeX-main-Iw} .MJXc-TeX-main-R {font-family: MJXc-TeX-main-R,MJXc-TeX-main-Rw} .MJXc-TeX-math-I {font-family: MJXc-TeX-math-I,MJXc-TeX-math-Ix,MJXc-TeX-math-Iw} .MJXc-TeX-size1-R {font-family: MJXc-TeX-size1-R,MJXc-TeX-size1-Rw} .MJXc-TeX-size2-R {font-family: MJXc-TeX-size2-R,MJXc-TeX-size2-Rw} .MJXc-TeX-size3-R {font-family: MJXc-TeX-size3-R,MJXc-TeX-size3-Rw} .MJXc-TeX-size4-R {font-family: MJXc-TeX-size4-R,MJXc-TeX-size4-Rw} @font-face {font-family: MJXc-TeX-ams-R; src: local('MathJax_AMS'), local('MathJax_AMS-Regular')} @font-face {font-family: MJXc-TeX-ams-Rw; src /*1*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/eot/MathJax_AMS-Regular.eot'); src /*2*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/woff/MathJax_AMS-Regular.woff') format('woff'), url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/otf/MathJax_AMS-Regular.otf') format('opentype')} @font-face {font-family: MJXc-TeX-cal-B; src: local('MathJax_Caligraphic Bold'), local('MathJax_Caligraphic-Bold')} @font-face {font-family: MJXc-TeX-cal-Bx; src: local('MathJax_Caligraphic'); font-weight: bold} @font-face {font-family: MJXc-TeX-cal-Bw; src /*1*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/eot/MathJax_Caligraphic-Bold.eot'); src /*2*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/woff/MathJax_Caligraphic-Bold.woff') format('woff'), url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/otf/MathJax_Caligraphic-Bold.otf') format('opentype')} @font-face {font-family: MJXc-TeX-frak-R; src: local('MathJax_Fraktur'), local('MathJax_Fraktur-Regular')} @font-face {font-family: MJXc-TeX-frak-Rw; src /*1*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/eot/MathJax_Fraktur-Regular.eot'); src /*2*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/woff/MathJax_Fraktur-Regular.woff') format('woff'), url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/otf/MathJax_Fraktur-Regular.otf') format('opentype')} @font-face {font-family: MJXc-TeX-frak-B; src: local('MathJax_Fraktur Bold'), local('MathJax_Fraktur-Bold')} @font-face {font-family: MJXc-TeX-frak-Bx; src: local('MathJax_Fraktur'); font-weight: bold} @font-face {font-family: MJXc-TeX-frak-Bw; src /*1*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/eot/MathJax_Fraktur-Bold.eot'); src /*2*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/woff/MathJax_Fraktur-Bold.woff') format('woff'), url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/otf/MathJax_Fraktur-Bold.otf') format('opentype')} @font-face {font-family: MJXc-TeX-math-BI; src: local('MathJax_Math BoldItalic'), local('MathJax_Math-BoldItalic')} @font-face {font-family: MJXc-TeX-math-BIx; src: local('MathJax_Math'); font-weight: bold; font-style: italic} @font-face {font-family: MJXc-TeX-math-BIw; src /*1*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/eot/MathJax_Math-BoldItalic.eot'); src /*2*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/woff/MathJax_Math-BoldItalic.woff') format('woff'), url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/otf/MathJax_Math-BoldItalic.otf') format('opentype')} @font-face {font-family: MJXc-TeX-sans-R; src: local('MathJax_SansSerif'), local('MathJax_SansSerif-Regular')} @font-face {font-family: MJXc-TeX-sans-Rw; src /*1*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/eot/MathJax_SansSerif-Regular.eot'); src /*2*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/woff/MathJax_SansSerif-Regular.woff') format('woff'), url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/otf/MathJax_SansSerif-Regular.otf') format('opentype')} @font-face {font-family: MJXc-TeX-sans-B; src: local('MathJax_SansSerif Bold'), local('MathJax_SansSerif-Bold')} @font-face {font-family: MJXc-TeX-sans-Bx; src: local('MathJax_SansSerif'); font-weight: bold} @font-face {font-family: MJXc-TeX-sans-Bw; src /*1*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/eot/MathJax_SansSerif-Bold.eot'); src /*2*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/woff/MathJax_SansSerif-Bold.woff') format('woff'), url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/otf/MathJax_SansSerif-Bold.otf') format('opentype')} @font-face {font-family: MJXc-TeX-sans-I; src: local('MathJax_SansSerif Italic'), local('MathJax_SansSerif-Italic')} @font-face {font-family: MJXc-TeX-sans-Ix; src: local('MathJax_SansSerif'); font-style: italic} @font-face {font-family: MJXc-TeX-sans-Iw; src /*1*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/eot/MathJax_SansSerif-Italic.eot'); src /*2*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/woff/MathJax_SansSerif-Italic.woff') format('woff'), url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/otf/MathJax_SansSerif-Italic.otf') format('opentype')} @font-face {font-family: MJXc-TeX-script-R; src: local('MathJax_Script'), local('MathJax_Script-Regular')} @font-face {font-family: MJXc-TeX-script-Rw; src /*1*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/eot/MathJax_Script-Regular.eot'); src /*2*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/woff/MathJax_Script-Regular.woff') format('woff'), url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/otf/MathJax_Script-Regular.otf') format('opentype')} @font-face {font-family: MJXc-TeX-type-R; src: local('MathJax_Typewriter'), local('MathJax_Typewriter-Regular')} @font-face {font-family: MJXc-TeX-type-Rw; src /*1*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/eot/MathJax_Typewriter-Regular.eot'); src /*2*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/woff/MathJax_Typewriter-Regular.woff') format('woff'), url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/otf/MathJax_Typewriter-Regular.otf') format('opentype')} @font-face {font-family: MJXc-TeX-cal-R; src: local('MathJax_Caligraphic'), local('MathJax_Caligraphic-Regular')} @font-face {font-family: MJXc-TeX-cal-Rw; src /*1*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/eot/MathJax_Caligraphic-Regular.eot'); src /*2*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/woff/MathJax_Caligraphic-Regular.woff') format('woff'), url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/otf/MathJax_Caligraphic-Regular.otf') format('opentype')} @font-face {font-family: MJXc-TeX-main-B; src: local('MathJax_Main Bold'), local('MathJax_Main-Bold')} @font-face {font-family: MJXc-TeX-main-Bx; src: local('MathJax_Main'); font-weight: bold} @font-face {font-family: MJXc-TeX-main-Bw; src /*1*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/eot/MathJax_Main-Bold.eot'); src /*2*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/woff/MathJax_Main-Bold.woff') format('woff'), url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/otf/MathJax_Main-Bold.otf') format('opentype')} @font-face {font-family: MJXc-TeX-main-I; src: local('MathJax_Main Italic'), local('MathJax_Main-Italic')} @font-face {font-family: MJXc-TeX-main-Ix; src: local('MathJax_Main'); font-style: italic} @font-face {font-family: MJXc-TeX-main-Iw; src /*1*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/eot/MathJax_Main-Italic.eot'); src /*2*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/woff/MathJax_Main-Italic.woff') format('woff'), url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/otf/MathJax_Main-Italic.otf') format('opentype')} @font-face {font-family: MJXc-TeX-main-R; src: local('MathJax_Main'), local('MathJax_Main-Regular')} @font-face {font-family: MJXc-TeX-main-Rw; src /*1*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/eot/MathJax_Main-Regular.eot'); src /*2*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/woff/MathJax_Main-Regular.woff') format('woff'), url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/otf/MathJax_Main-Regular.otf') format('opentype')} @font-face {font-family: MJXc-TeX-math-I; src: local('MathJax_Math Italic'), local('MathJax_Math-Italic')} @font-face {font-family: MJXc-TeX-math-Ix; src: local('MathJax_Math'); font-style: italic} @font-face {font-family: MJXc-TeX-math-Iw; src /*1*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/eot/MathJax_Math-Italic.eot'); src /*2*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/woff/MathJax_Math-Italic.woff') format('woff'), url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/otf/MathJax_Math-Italic.otf') format('opentype')} @font-face {font-family: MJXc-TeX-size1-R; src: local('MathJax_Size1'), local('MathJax_Size1-Regular')} @font-face {font-family: MJXc-TeX-size1-Rw; src /*1*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/eot/MathJax_Size1-Regular.eot'); src /*2*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/woff/MathJax_Size1-Regular.woff') format('woff'), url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/otf/MathJax_Size1-Regular.otf') format('opentype')} @font-face {font-family: MJXc-TeX-size2-R; src: local('MathJax_Size2'), local('MathJax_Size2-Regular')} @font-face {font-family: MJXc-TeX-size2-Rw; src /*1*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/eot/MathJax_Size2-Regular.eot'); src /*2*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/woff/MathJax_Size2-Regular.woff') format('woff'), url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/otf/MathJax_Size2-Regular.otf') format('opentype')} @font-face {font-family: MJXc-TeX-size3-R; src: local('MathJax_Size3'), local('MathJax_Size3-Regular')} @font-face {font-family: MJXc-TeX-size3-Rw; src /*1*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/eot/MathJax_Size3-Regular.eot'); src /*2*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/woff/MathJax_Size3-Regular.woff') format('woff'), url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/otf/MathJax_Size3-Regular.otf') format('opentype')} @font-face {font-family: MJXc-TeX-size4-R; src: local('MathJax_Size4'), local('MathJax_Size4-Regular')} @font-face {font-family: MJXc-TeX-size4-Rw; src /*1*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/eot/MathJax_Size4-Regular.eot'); src /*2*/: url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/woff/MathJax_Size4-Regular.woff') format('woff'), url('https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/fonts/HTML-CSS/TeX/otf/MathJax_Size4-Regular.otf') format('opentype')} skip to content

se.moevm.info User Tools Log In

Site Tools Search ToolsShow pagesourceOld revisionsBacklinksRecent ChangesMedia ManagerSitemapLog In> Recent Changes

Media Manager

Sitemap

You are here: МОЭВМ Вики » Курсы » Вычислительная математика » Практическая работа №11: Решение системы линейных уравнений −Sidebar Сотрудникам

Дипломникам

Курсы Программирование

Информатика

Вычислительная математика

Объектно-ориентированное программирование

Построение и анализ алгоритмов

Разработка ПО с GUI

Введение в программную инженерию

Базы знаний и экспертные системы

Функциональное программирование

Технологии хранения данных

Проектирование человеко-машинного интерфейса

Теория принятия решений

Анализ, моделирование и оптимизация систем

Анализ и интерпретация данных

Robot OS

Представление знаний и системы искусственного интеллекта

МДП

AI Systems practice

Введение в нереляционные базы данных

Разработка приложений для мобильных платформ

Автоматизация учебных задач

Задачи для практики 3 курс 2017г

Написание научных статей

Учебные материалы по работе со Stepik

Конференция ППС

Список конференций

Отправка отчетов

Магистрам

Аспирантам

Summer Schools

FAQ

courses:computational_mathematics:task11 −Table of Contents Практическая работа №11: Решение системы линейных уравнений Цель работы

Основные теоретические положения Решение систем линейных алгебраических уравнений методом Гаусса

Решение систем линейных алгебраических уравнений методом простой итерации

Постановка задачи

Порядок выполнения работы

Содержание отчёта

Практическая работа №11: Решение системы линейных уравнений Цель работы Исследование и реализация различных методов решения систем линейных алгебраических уравнений.

Основные теоретические положения Методы решения систем линейных алгебраических уравнений (СЛАУ) делятся на две группы. К первой группе принадлежат так называемые точные, или прямые, методы – алгоритмы, позволяющие получить решение системы за конечное число арифметических действий. Сюда относятся известное правило Крамера нахождения решения с помощью определителей, метод Гаусса (метод исключений) и метод прогонки. Правило Крамера при реализации на ЭВМ не применяется ввиду значительно большего по сравнению с методом Гаусса числа арифметических действий. Метод Гаусса используется при решении систем до порядка 103. Метод прогонки применяется для решения важного класса специальных систем линейных уравнений с трехдиагональной матрицей, часто возникающей в практических приложениях.

Решение систем линейных алгебраических уравнений методом Гаусса Рассматривается СЛАУ nnn-го порядка ⎧⎪ ⎪ ⎪⎨⎪ ⎪ ⎪⎩a11x1+a12x2+⋯+a1nxn=b1,a21x1+a22x2+⋯+a2nxn=b2,……………………………an1x1+an2x2+⋯+annxn=bn,{a11x1+a12x2+⋯+a1nxn=b1,a21x1+a22x2+⋯+a2nxn=b2,……………………………an1x1+an2x2+⋯+annxn=bn, \left\{ \begin{aligned} a_{11}x_1 + a_{12}x_2 + \dots + a_{1n}x_n &= b_1,\\ a_{21}x_1 + a_{22}x_2 + \dots + a_{2n}x_n &= b_2,\\ \dots\dots\dots\dots\dots\dots\dots\dots\dots&\dots\dots\\ a_{n1}x_1 + a_{n2}x_2 + \dots + a_{nn}x_n &= b_n, \end{aligned} \right. что в векторном виде записывается как Ax=bAx=bAx = b.

Суть метода исключения по главным элементам (метод Гаусса) заключается в следующем. Находится наибольший по абсолютной величине коэффициент akjakja_{kj}. Для исключения xjxjx_j из iii-го уравнения (i≠ki≠ki \ne k) необходимо умножить kkk-е уравнение на aij/akjaij/akja_{ij}/a_{kj} и вычесть его из iii-го уравнения, после чего процесс повторяется для исключения другого неизвестного из оставшихся n−1n−1n-1 уравнений и т.д. В результате система уравнений приводится к треугольному виду ⎧⎪ ⎪ ⎪⎨⎪ ⎪ ⎪⎩x1+α12x2+⋯+α1nxn=β1,x2+⋯+α