Question

Which of the following shows a matrix and its inverse?

Answer 1

To find the inverse matrix, augment it with the identity matrix and perform row operations trying to make the identity matrix to the left. Then to the right will be the inverse matrix.

`\mleft[\begin{array}cc-2 & 1 & 1 & 0 \\ 0 & -3 & 0 & 1\end{array}\mright]`
`\begin{gathered} R_1=(R_(1))/(2)\mleft[\begin{array}cc1 & -(1)/(2) & (1)/(2) & 0 \\ 0 & -3 & 0 & 1\end{array}\mright] \\ R_2=(R_(2))/(3)\mleft[\begin{array}cc1 & -(1)/(2) & (1)/(2) & 0 \\ 0 & 1 & 0 & -(1)/(3)\end{array}\mright] \\ R_1=R_1+(R_(2))/(2)\mleft[\begin{array}cc1 & 0 & (1)/(2) & (1)/(6) \\ 0 & 1 & 0 & (1)/(3)\end{array}\mright] \end{gathered}`

These corresponds to:

`\mleft[\begin{array}{cc}2 & -1 \\ 0 & 3\end{array}\mright]\mleft[\begin{array}{cc}(1)/(2) & (1)/(6) \\ 0 & (1)/(3)\end{array}\mright]`