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:

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

$\det A = -2 ((-9)\times6-(-8)\times(-5)) + ((-4)\times6 - (-3)\times(-5)) \\ ~~~~~~~~~~~~~~~- 15 ((-4)\times(-8)-(-3)\times(-9))$

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

$\det A = \boxed{74}$