Question

What Is the inverse of.. (ignore pencil writing) -matrices- (there may be more than one answer

Answer 1

`A^(-1)\text{ =}\begin{bmatrix}{2} & {-5} & {} \\ {-1} & {3} & {} \\ {} & {} & {}\end{bmatrix}\text{ (option B)}`

Step-by-step explanation:
`\begin{bmatrix}{3} & {5} & {} \\ {1} & {2} & {} \\ {} & {} & {}\end{bmatrix}`

To find the inverse of the matrix, first let's find the determinant:

`\begin{gathered} |A|\text{ = 3(2) - 5(1)} \\ |A|\text{ = 6 - 5} \\ |A|\text{ = 1} \end{gathered}`

Then, we'll find the Adjunct of the matrix:

`\begin{gathered} \begin{bmatrix}{3} & {5} & {} \\ {1} & {2} & {} \\ {} & {} & {}\end{bmatrix}\text{ : interchange }3\text{ and 2. negate 1 and 5} \\ \text{Adjunct = }\begin{bmatrix}{2} & {-5} & {} \\ {-1} & {3} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}`
`\begin{gathered} In\text{verse of the matrix = }(1)/(|A|)*\text{ adjunct} \\ A^(-1)\text{ = }(1)/(1)(\begin{bmatrix}{2} & {-5} & {} \\ {-1} & {3} & {} \\ {} & {} & {}\end{bmatrix}) \\ A^(-1)\text{ =}\begin{bmatrix}{2} & {-5} & {} \\ {-1} & {3} & {} \\ {} & {} & {}\end{bmatrix}\text{ (option B)} \\ \end{gathered}`