Question

.Find the inverse of A if it has one, or state that the inverse does not exist.

Answer 1

Step-by-step explanation:

Find the discriminant

$|a| = ad - bc$

for a matrix

(a b)

(c d)

Here it is

$( - 6)( - 2) - 0(5)$

$12 - 0 = 12$

The formula for the inverse of a 2 by 2 matrix,

$\frac{1}{ad - bc} \binom{d}{ - c} \binom{ - b}{a}$

Note since the discriminant isn't 0, an inverse must exist.

$\frac{1}{12} \binom{ - 2}{ - 5} \binom{ 0}{ - 6}$

Multiply everything by the fraction.

$\binom{ - \frac{1}{6} }{ \frac{ - 5}{12} } \binom{ 0 }{ - \frac{1}{2} }$

The last matrix is the inverse of A