Answer to Question #311845 in Linear Algebra for Showi

Question

Solve for the determinant in the equation below.

4 −3 2

1 2 −2

2 -1 −4

Answer 1

Solution

Given that

$det(A)=\begin{vmatrix} 4 & -3 & 2\\ 1 & 2 & -2\\ 2 & -1 & -4 \end{vmatrix}$

$det(A)=4\begin{vmatrix} 2 & -2 \\ -1 & -4 \end{vmatrix}-(-3)\begin{vmatrix} 1 & -2 \\ 2 & -4 \end{vmatrix}+2\begin{vmatrix} 1 & 2 \\ 2 & -1 \end{vmatrix}$

$det(A)=4(-8-2)+3(-4+4)+2(-1-4)$

$det(A)=$ $4(-10)+3(0)+2(-5)$

$det(A)=-40+0-10$

$det(A)=-50$