Question

Find the value of the determinant.

|2 7 -3|
|-1 5 -4|
|6 9 0 |

Answer 1

$$
\left[
\begin{matrix}
2 & 7 & -3\\
-1 & 5& -4\\
6 & 9 & 0
\end{matrix}
\right] \implies
-3(+1)
\left[
\begin{matrix}
-1& 5\\
6 & 9
\end{matrix}
\right]
-4(-1)
\left[
\begin{matrix}
2& 7\\
6& 9
\end{matrix}
\right]\\
-3(-9-30)+4(18-42)\\
-3(-39)+4(24) \implies 21
$$

Answer 2

$$
\left[
\begin{matrix}
2 & 7 & -3\\
-1 & 5& -4\\
6 & 9 & 0
\end{matrix}
\right] \implies
-3(+1)
\left[
\begin{matrix}
-1& 5\\
6 & 9
\end{matrix}
\right]
-4(-1)
\left[
\begin{matrix}
2& 7\\
6& 9
\end{matrix}
\right]\\
-3(-9-30)+4(18-42)\\
-3(-39)+4(-24) \implies 21
$$

Answer 3

better, tis -24