sss / 14_Кириллова Ксения_кр1.doc
.docxКонтрольная работа вариант 1
упражнение 3
>> A=[3 5 1;5 1 3;1 3 5]
A =
3 5 1
5 1 3
1 3 5
>> res=A(1,1).*A(2,2).*A(3,3)+A(2,1).*A(3,2).*A(1,3)+A(1,2).*A(2,3).*A(3,1)-A(1,3).*A(2,2).*A(3,1)-A(1,1).*A(3,2).*A(2,3)-A(2,1).*A(1,2).*A(3,3)
res =
-108
>> B=[-6; 6; 0]
B =
-6
6
0
>> B1=[B,A(:,2),A(:,3)]
B1 =
-6 5 1
6 1 3
0 3 5
>> res=A(1,1).*A(2,2).*A(3,3)+A(2,1).*A(3,2).*A(1,3)+A(1,2).*A(2,3).*A(3,1)-A(1,3).*A(2,2).*A(3,1)-A(1,1).*A(3,2).*A(2,3)-A(2,1).*A(1,2).*A(3,3)
res =
-108
>> A1=B1
A1 =
-6 5 1
6 1 3
0 3 5
>> res1=A1(1,1).*A1(2,2).*A1(3,3)+A1(2,1).*A1(3,2).*A1(1,3)+A1(1,2).*A1(2,3).*A1(3,1)-A1(1,3).*A1(2,2).*A1(3,1)-A1(1,1).*A1(3,2).*A1(2,3)-A1(2,1).*A1(1,2).*A1(3,3)
res1 =
-108
>> A2=[A(:,1),B,A(:,3)]
A2 =
3 -6 1
5 6 3
1 0 5
>> res2=A2(1,1).*A2(2,2).*A2(3,3)+A2(2,1).*A2(3,2).*A2(1,3)+A2(1,2).*A2(2,3).*A2(3,1)-A2(1,3).*A2(2,2).*A2(3,1)-A2(1,1).*A2(3,2).*A2(2,3)-A2(2,1).*A2(1,2).*A2(3,3)
res2 =
216
>> A3=[A(:,1),A(:,2),B]
A3 =
3 5 -6
5 1 6
1 3 0
>> res3=A3(1,1).*A3(2,2).*A3(3,3)+A3(2,1).*A3(3,2).*A3(1,3)+A3(1,2).*A3(2,3).*A3(3,1)-A3(1,3).*A3(2,2).*A3(3,1)-A3(1,1).*A3(3,2).*A3(2,3)-A3(2,1).*A3(1,2).*A3(3,3)
res3 =
-108
>> x1=res1/res
x1 =
1
>> x2=res2/res
x2 =
-2
>> x3=res3/res
x3 =
ПРОВЕРКА
>> a=3*x1+5*x2+x3
a =
-6
>> b=5*x1+x2+3*x3
b =
6
>> c=x1+3*x2+5*x3
c =
0
упражнение 1
>> A=[1 -3 1;4 2 -1;1 0 2]
A =
1 -3 1
4 2 -1
1 0 2
>> x=[-9 -3 1;-8 2 -1;3 0 2]
x =
-9 -3 1
-8 2 -1
3 0 2
>> y=[1 -9 1;4 -8 -1; 1 3 2]
y =
1 -9 1
4 -8 -1
1 3 2
>> z=[1 -3 -9;4 2 -8;1 0 3]
z =
1 -3 -9
4 2 -8
1 0 3
>> dx=det(A)
dx =
29
>> dx=det(x)
dx =
-81
>> dy=det(y)
dy =
88
>> dz=det(z)
dz =
84
>> dA=det(A)
dA =
29
>> x1=dx/dA
x1 =
-2.7931
>> y1=dy/dA
y1 =
3.0345
>> z1=dz/dA
z1 =
2.8966
>> X=-2.7931*a+3.0345*b+ 2.8966*c
Упражнение 2
> A=[2 3 4]
A =
2 3 4
>> B=[-5 1 0]
B =
-5 1 0
>> B(1)-A(1)
ans =
-7
Ответ на задание А:>> AB=[B(1)-A(1),B(2)-A(2),B(3)-A(3)]
AB =
-7 -2 -4
>> D=[-3 0 5]
D =
-3 0 5
>> AD=[D(1)-A(1),D(2)-A(2),D(3)-A(3)]
AD =
-5 -3 1
>> scalar = sum(AB.*AD)
scalar =
37
>> dl=sqrt(AD(1)^2+AD(2)^2+AD(3)^2)
dl =
5.9161
>> Proekciya=scalar/dl
Proekciya =
6.2541
>>
ОТВЕТ на задание Б:
>> AB
AB =
-7 -2 -4
>> C=[2 7 1]
C =
2 7 1
>> AC=[C(1)-A(1),C(2)-A(2),C(3)-A(3)]
AC =
0 4 -3
>> Proiz=cross(AB,AC)
Proiz =
22 -21 -28
>> dl1=sqrt(Proiz(1)^2+Proiz(2)^2+Proiz(3)^2)
dl1 =
41.3401
>> S=0.5*dl1
S =
20.6700
>>