Find the inverse of the matrices given below. [(8,-4,1)(10,0,6)(8,1,6)]

Question

Find the inverse of the matrices given below.

\(\begin{bmatrix} 8 & -4 & 1 \\[0.3em] 10 & 0 & 6 \\[0.3em] 8 & 1 & 6 \end{bmatrix}\)

[(8,-4,1)(10,0,6)(8,1,6)]

Answer 1

We have, A = \(\begin{bmatrix} 8 & -4 & 1 \\[0.3em] 10& 0 & 6\\[0.3em] 8 &1 & 6 \end{bmatrix}\)

We have to find A ^-1 and A^-1 = \(\frac{adj\,A}{|A|}\)

Firstly, we find |A|

Expanding |A| along C₁, we get

= 8(0 – 6) – 10(-24 – 1) + 8(-24 – 0) 

= 8(-6) – 10(-25) + 8(-24) 

= -48 + 250 – 192 

= 250 – 240 

= 10

Now, we have to find adj A and for that we have to find co-factors:

\(\frac{1}{10}.\begin{bmatrix} -6 & 25& -24 \\[0.3em] -12 & 40 &-38 \\[0.3em] 10 & -40 & 40 \end{bmatrix}\)