На сортировку / 1 / ЭЭФ / Новая папка (2) / k Маткад лаба №1 №2Kazhymukan
.docxMINISTRY OF EDUCATION AND SCIENCE OF THE REPUBLIC OF KAZAKHSTAN
Almaty University of Power Engineering and Telecommunications
Department of Higher Mathematics
Numerical methods and computer realization
Laboratory work №1,2
Subject: Solution of tasks of elementary mathematics
Tasks of vector and linear algebra
Option №1
Done by: the student of group EE-14-1
Akhmet Z.
Checked by: Zhanuzakova D.T.
Almaty, 2015
Laboratory work №1
1 Task. Calculate:
After a set of expression from the keyboard, press "=". The result will appear on the screen
Answer: 12
2 Task. Simplify the expression:
The job (on screen):
After a set of expressions with the keyboard, highlight the blue corner cursor, then click on the character position in the main menu, Mathcad, and further along the line Simplify.
Answer:
3 Task. Expand the brackets and cause similar terms.
The job (on screen):
After a set of expressions with the keyboard, highlight it in blue angular cursor, click the position of the character, and then expand.
Answer: b4-1
4 Task. To factor the expression:
The job (on screen):
After a set of expressions with the keyboard, highlight it in blue angular cursor, click the position of the character, and then factor.
Answer: (x-1)(x2-x+3)(x2+x+3)
5 Task. Decomposed into partial fractions:
After a set of expressions with the keyboard, highlight the blue corner cursor variable x, click the character position, select the line of variables, and then click Convert to partial fractions.
6 Task. Solve the equation:
The job (on screen):
To solve this equation we need to click the Symbolic Math operators on the panel, and then on the button Solve and left the word to enter the equation F(x)=0, and the right - the name of the variable with respect to which it is necessary to solve the equation. Click on empty space on the page.
Answer: 1;
Laboratory work №2
1
Task. Given
vectors
and
the numbers
k, m, n.
Search:
1)
;
2)
;
3)
scalar product
and
4)
vector
product
and
;
5)
the
length of the vector
and the vector obtained in the preceding paragraph;
6)
mixed
product
,
and
7) Whether given three vectors are linearly dependent or not? Can they form a basis of the space?
1.
Given
vectors а(3,-2,1),
b(0,2,-3),
c(-3,2,-1)
and
the number of
.
Find:
;
The job (on screen):
We
define
vector in a matrix - column::
Answer:
,
and numbers
Find
the vector
;
Answer:
3.
Find the scalar
product
of vectors
and
.
The job (on screen):
Answer:
4.
Find the vector product of vectors
and
.
The job (on screen):
To enter the vector product: Mathematics Panel click Vector and matrix operations on the toolbar that appears click the Matrix Vector product and enter the factors. Select the entire expression angular blue cursor and press the equal sign on the keyboard. Векторное произведение (Gross Product)
Answer:
5.
Find
the length
of the vector
and the vector obtained in the preceding paragraph.
The job (on screen):
Answer:
,
6.
Find
the mixed
product
,
and
The job (on screen):
Answer: 0
7. Whether given three vectors are linearly dependent or not? Can they form a basis of the space?
The job (on screen):
Answer: The vectors are linearly dependent. The determinant of the vectors equal to 0. This means they can not form a basis for the space.
2 Task. Given the matrix A, B, C;
1) Find the determinant of A and C
2)
Determine
the matrix
;
3) Find the matrix inverse matrix A and C, if they exist;
4) Find the ranks of the matrices A and C using the rank (A);
5)
Determine
the matrix
.
1. Find the determinant of A and C.
The job (on screen):
Answer:
,
2.
Determine the matrix
.
The job (on screen):
Target using the Transpose of the matrix panel of the Matrix
Answer:
3 Find the matrix inverse matrix A and C.
The job (on screen):
The task runs using the Matrix Inversion panel.
Answer:
4. Find the ranks of the matrices A and C using the rank (A).
The job (on screen):
Answer:
3
5.
.
The job (on screen):
Answer:
3 Task. Given a system of equations DX=F.
1) Solve the system of equations by Cramer's rule;
2)
Solve
the system of equations by using the inverse matrix by the formula
;
3) Solve the system of equations by means of the operation (in the built-
Mathcad functions) lsolve (D,F).
-
Solve the system of equations by Cramer's rule.
The job (on screen):
Determinant
of system:
The determinant of the system is not equal to zero, so the system has a unique solution.
We determine the determinants of support:
Answer: -0.345, 0.65, -0.803, -0.567.
2.
This system of equations is ready by the inverse matrix by the
formula
The job (on screen):
Answer: -0.345, 0.65, -0.803, -0.567.
-
Solve the same system with a built-in function lsolve (D,F).
The job (on screen):
Answer: -0.345, 0.65, -0.803, -0.567.