HW06 Problem 2 Previous Problem List Next 1 point Suppose th

HW-06: Problem 2 Previous Problem List Next (1 point) Suppose that: 5-45 1-4 A= and B =| 4-1 | 4 5 -5-4-4 Given the following descriptions, determine the following elementary matrices and their inverses.

Solution

Write the augmented matrix

Make the pivot in the 1st column by dividing the 1st row by 5

Multiply the 1st row by 4

Subtract the 1st row from the 2nd row and restore it

Multiply the 1st row by -5

Subtract the 1st row from the 3rd row and restore it

Make the pivot in the 2nd column by dividing the 2nd row by 11/5

Multiply the 2nd row by -4/5

Subtract the 2nd row from the 1st row and restore it

Multiply the 2nd row by -8

Subtract the 2nd row from the 3rd row and restore it

Make the pivot in the 3rd column by dividing the 3rd row by -109/11

Multiply the 3rd row by -1/11

Subtract the 3rd row from the 1st row and restore it

Multiply the 3rd row by -15/11

Subtract the 3rd row from the 2nd row and restore it

There is the inverse matrix on the right

	A1	A2	A3	A1	A2	A3
1	5	-4	5	1	0	0
2	4	-1	1	0	1	0
3	-5	-4	-4	0	0	1