# How do you find the inverse of [(11,-5), (2,-1)]?

Apr 25, 2018

Append an identity matrix to the right.
Use elementary row operations to make the matrix on the left until it becomes an identity matrix; this will make the right will become the inverse matrix.

#### Explanation:

Given:
[ (11,-5), (2,-1) ]

Append an identity matrix to the right:

[ (11,-5,|,1,0), (2,-1,|,0,1) ]

Use elementary row operations:

${R}_{1} - 5 {R}_{2} \to {R}_{1}$:

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

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

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

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

[ (1,0,|,1,-5), (0,1,|,2,-11) ]

The inverse is the matrix on the right:

[ (1,-5), (2,-11) ]