For each of the following matrices use row reduction to find

For each of the following matrices, use row reduction to find the inverse or show that the inverse does not exist: M = [-1 1 -2 3] N = [1 -2 -1 -1 2 1 0 3 2] P = [1 0 -1 3 -2 -4 -1 2 2]

Solution

b) M =

Your matrix

Determinant is not zero, therefore inverse matrix exists

Write the augmented matrix

Find the pivot in the 1st column in the 1st row (inversing the sign in the whole row)

Eliminate the 1st column

Find the pivot in the 2nd column in the 2nd row

Eliminate the 2nd column

There is the inverse matrix on the right

solution

b)

N =

Your matrix

Your matrix

Eliminate elements in the 1st column under the 1st element

Multiply the main diagonal elements

1 x 0 x 2 = 0

solution

Determinant is 0

Determinant is zero, therefore inverse matrix does not exist

C)

P =

Your matrix

Your matrix

Eliminate elements in the 1st column under the 1st element

Eliminate elements in the 2nd column under the 2nd element

Multiply the main diagonal elements

1 x (-2) x 0 = 0

solution

Determinant is 0

Determinant is zero, therefore inverse matrix doesn\'t exist

	A1	A2
1	-1	-2
2	1	3