Question

What is the determinant of the coefficient matrix of the system -x-y-z=-3-x-y-z=83x+2y+z= 0

Answer 1

Answer:

The determinant of the coefficient matrix = 0

Explanation:

The given system of equations is:

-x - y - z=-3

-x - y - z=8

3x + 2y + z = 0

The coefficient matrix is:

$D\text{ = }\begin{bmatrix}{-1} & {-1} & {-1} \\ {-1} & {-1} & {-1} \\ {3} & {2} & {1}\end{bmatrix}$

The determinant of the coefficient matrix is:

$\begin{gathered} |D|=-1(-1+2)+1(-1+3)-1(-2+3) \\ |D|=-1(1)+1(2)-1(1) \\ |D|=-1+2-1 \\ |D|=0 \end{gathered}$

The determinant of the coefficient matrix = 0