Question

What is the determinant of the coefficient matrix of the system 0 16 18 40

Answer 1

A

Explanation:

Answer 2

The coefficient matrix is

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

Notice that the last row is -4 times the first row, so that the rows of the matrix are not independent. This means the determinant would be 0.

Just to confirm, we can compute the determinant via a Laplace expansion along the first row:

`\begin{vmatrix}-1&-1&2\\3&2&-1\\4&4&-8\end{vmatrix}=-\begin{vmatrix}2&-1\\4&-8\end{vmatrix}+\begin{vmatrix}3&-1\\4&-8\end{vmatrix}+2\begin{vmatrix}3&2\\4&4\end{vmatrix}`

`=-(-16+4)+(-24+4)+2(12-8)=12-20+8=0`