Question

Find the

-2
-4
-3
-1
-9-8
determinant OF
-15
- 5
6

Answer 1

Determinants are defined only for square matrices, so I assume you are given the 3×3 matrix

`A = \begin{bmatrix}-2 & -4 & -3 \\ -1 & -9 & -8 \\ -15 & -5 & 6 \end{bmatrix}`

Let's compute the determinant by taking the cofactor expansion along the first column:

`\det A = -2 \det\begin{bmatrix}-9 & -8 \\ -5 & 6\end{bmatrix} + \det\begin{bmatrix}-4 & -3 \\ -5 & 6\end{bmatrix} - 15 \det \begin{bmatrix}-4 & -3 \\ -9 & -8\end{bmatrix}`

`\det A = -2 ((-9)*6-(-8)*(-5)) + ((-4)*6 - (-3)*(-5)) \\ ~~~~~~~~~~~~~~~- 15 ((-4)*(-8)-(-3)*(-9))`

`\det A = -2(-54-40) + (-24 - 15) - 15 (32 - 27)`

`\det A = \boxed{74}`