Question

Find the inverse of each of the matrices(if it exists). \(\begin{bmatrix}1&2&3\\0&2&4\\0&0&5\end{bmatrix}\)

Answer 1

Let A=\(\begin{bmatrix}1&2&3\\0&2&4\\0&0&5\end{bmatrix}\)

We have, IAI=1(10-0)-2(0-0)+3(0-0)=10
A₁₁=10-0=10, A₁₂=-(0-0)=0,A₁₃=0-0=0
A₂₁=-(10-0)=-10, A₂₂=5-0=5, A₂₃=-(0-0)=0
A₃₁=8-6=2 ,A₃₂=-(4-0)=-4,A₃₃=2-0=2

adj A=\(\begin{bmatrix}10&-10&2\\0&5&-4\\0&0&2\end{bmatrix}\)

so A^-1=\(\frac{1}{\mid A \mid}\)adj A=\(\frac{1}{10}\begin{bmatrix}10&-10&2\\0&5&-4\\0&0&2\end{bmatrix}\)