Question

Find the inverse of each of the following matrices.

(i) (\begin{bmatrix} 0 & 1 & -1\[0.3em] 4&-3 &4 \ 3 & -3 & 4\end{bmatrix})

(ii) (\begin{bmatrix} 0 & 0 & -1\[0.3em] 3&4 & 5 \ -2 & -4 & -7\end{bmatrix})

Answer 1

(i) Criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| =

= 0 – 1 (16 – 12) – 1 (– 12 + 9)

= – 4 + 3

= – 1

So, A – 1 exists

Co-factors of A are

C11 = 0

C21 = – 1

C31 = 1

C12 = – 4

C22 = 3

C32 = – 4

C13 = – 3

C23 = 3

C33 = – 4

(ii)Criteria of existence of inverse matrix is the determinant of a given matrix should not equal to zero.

|A| =

= 0 – 0 – 1(– 12 + 8)

= 4

So, A – 1 exists

Co-factors of A are

C11 = – 8

C21 = 4

C31 = 4

C12 = 11

C22 = – 2

C32 = – 3

C13 = – 4

C23 = 0

C33 = 0