Question

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

Answer 1

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:

`5R_1 and 2R_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) ]#

`3/2R_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) ]#