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

1 Answer
Apr 25, 2018

Answer:

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) ]#