This has four parts to it. the following system oflinear equations x - y =2z=13 2x +2y -z =-6 -x + 3y +z = -7 a) Provide a coefficient matrix corresponding to the system oflinear equations b) what is the inverse of this matrix? c) What is the transpose of the matrix? d) find the determinant for this matrix?

Livia Cardenas 2022-07-31 Answered
This has four parts to it. the following system of linear equations
x - y =2z=13
2x +2y -z =-6
-x + 3y +z = -7
a) Provide a coefficient matrix corresponding to the system oflinear equations
b) what is the inverse of this matrix?
c) What is the transpose of the matrix?
d) find the determinant for this matrix?
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Answers (1)

coolng90qo
Answered 2022-08-01 Author has 14 answers
a) [ 1 1 2 13 2 2 1 6 1 3 1 7 ]
b) [ 1 1 2 1 0 0 2 2 1 0 1 0 1 3 1 0 0 1 ] = [ 1 1 2 1 0 0 0 4 3 2 1 0 1 3 1 0 0 1 ] R 1 + R 2 R 2
[ 1 1 2 1 0 0 0 4 3 2 1 0 0 2 1 1 0 1 ] R 3 + R 1 R 3
[ 1 1 2 1 0 0 0 4 3 2 1 0 0 0 5 4 1 2 ] R 3 + R 2 R 3
[ 1 0 5 / 4 1 / 2 1 / 4 0 0 1 3 / 4 1 / 2 1 / 4 0 0 0 1 4 / 5 1 / 5 2 / 5 ] R 1 + R 2 R 1
[ 1 0 5 / 4 1 / 2 1 / 4 0 0 1 0 1 / 10 1 / 10 3 / 10 0 0 1 4 / 5 1 / 5 2 / 5 ] R 1 ( 3 / 4 ) R 3 R 2
Finally
R 1 + ( 5 / 4 ) R 3 R 1
that is your inverse
[ 1 0 0 1 / 2 1 / 2 1 / 2 0 1 0 1 / 10 1 / 10 3 / 10 0 0 1 4 / 5 1 / 5 2 / 5 ]
A = [ 1 1 2 2 2 1 1 3 1 ] , A 1 = [ 1 / 2 1 / 2 1 / 2 1 / 10 1 / 10 3 / 10 4 / 5 1 / 5 2 / 5 ]
c) transpose: A = A T
d) Det(A)=-10
Det(A)=1(2+3)+1(2-1)-2(6+2)=-10
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