Question

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

Answer 1

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_1-5R_2 to R_1`:

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

`-1R_2 to R_2`:

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

`R_2+2R_1 to R_2`:

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

The inverse is the matrix on the right:

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