Determine whether the following matrices are invertible and

Determine whether the following matrices are invertible and find the inverse, if it exists: a) [2 1 2 0 5 3 -1 1 0] b) [3 -6 -4 8] c) [1 3 2 -1 1 3 2 2 -1]

Solution

(a)Your matrix

Determinant is not zero, therefore inverse matrix exists

  

Write the augmented matrix

Find the pivot in the 1st column and swap the 2nd and the 1st rows

Eliminate the 1st column

Make the pivot in the 2nd column by dividing the 2nd row by -10

Eliminate the 2nd column

Make the pivot in the 3rd column by dividing the 3rd row by 1/10

Eliminate the 3rd column

There is the inverse matrix on the right

solution

B)

Your matrix

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

C)

Your matrix

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

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