Question

find the determinant of the matrix: (3x3)
[x 0 -4]
[3 x x^2] = ?
[-3 x 1]

Answer 1

\[D=\begin{vmatrix}x&0&-4\\
3&x&x^2\\-3&x&1\end{vmatrix}\]
Using a cofactor expansion along the first row, you have
\[\begin{align*}D&=x\begin{vmatrix}x&x^2\\x&1\end{vmatrix}-0\begin{vmatrix}3&x^2\\-3&1\end{vmatrix}-4\begin{vmatrix}3&x\\-3&x\end{vmatrix}\\\\\\
&=x\begin{vmatrix}x&x^2\\x&1\end{vmatrix}-4\begin{vmatrix}3&x\\-3&x\end{vmatrix}\end{align*}\]
Finding the determinant of a 2x2 is easy. Can you finish the work?

Answer 2

Yeah, thanks

Answer 3

yw