# How do you find the inverse of [(-2,3), (5,7)]?

##### 1 Answer
Dec 11, 2016

Concatenate an identity matrix onto the given matrix and do row operations, until the original matrix is an identity matrix.

#### Explanation:

Concatenate an identity matrix onto the given matrix:

[ (-2, 3, |, 1, 0), (5, 7,|,0,1) ]

Perform row operations until you obtain and identity matrix on the left:

$5 {R}_{1} \mathmr{and} 2 {R}_{2}$:

[ (-10, 15, |, 5, 0), (10, 14,|,0,2) ]

${R}_{1} + {R}_{2} \to {R}_{2}$:

[ (-10, 15, |, 5, 0), (0, 29,|,5,2) ]

${R}_{2} / 29 \to {R}_{2}$:

[ (-10, 15, |, 5, 0), (0, 1,|,5/29,2/29) ]

${R}_{1} / - 10 \to {R}_{1}$:

[ (1, -3/2, |, -1/2, 0), (0, 1,|,5/29,2/29) ]

$\frac{3}{2} {R}_{2} + {R}_{1} \to {R}_{1}$:

[ (1, 0, |, -7/29, 3/29), (0, 1,|,5/29,2/29) ]

The inverse matrix is on the right.

I will separate it for you:

[ (-7/29, 3/29), (5/29,2/29) ]