Question

What is the determinant of the coefficient matrix of the system

{-x-y+2z=5

{3x+2y-z=3

{4x+4y-8z=-2


A. 0

B. 16

C. 18

D. 40

Answer 1

The coefficient matrix is

`\begin{bmatrix}-1&-1&2\\3&2&-1\\4&4&-8\end{bmatrix}`

Its determinant is then

`\det\begin{bmatrix}-1&-1&2\\3&2&-1\\4&4&-8\end{bmatrix}=-4\det\begin{bmatrix}-1&-1&2\\3&2&-1\\-1&-1&2\end{bmatrix}`

which is equal to 0.