use determinants to find out if the matrix is invertible

use determinants to find out if the matrix is invertible


H
Asked by 2 years ago
240 points

In Exercises 21–23, use determinants to find out if the matrix is invertible. $$ \begin{vmatrix} 5 & 1 & -1 \\ 1 & -3 & -2 \\ 0 & 5 & 3 \end{vmatrix} $$

use determinants
hansel

1 Answer

Answered by 2 years ago
8.7k points

the determinant of the matrix is,

$$+5 \begin{vmatrix} -3 & -2 \\ 5 & 3 \end{vmatrix} -(1) \begin{vmatrix} 1 & -2 \\ 0 & 3 \end{vmatrix} +(-1)\begin{vmatrix} 1 & -3 \\ 0 & 5 \end{vmatrix}$$

$$ = 5(-9-(-10))-1(3-0)-1(5-0)) =5(1)-1(3)-1(5)=-3 \ne 0$$

hence the matrix is invertible since the determinant is non-zero

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Asked: 2 years ago

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