Question

How to find the inverse of a matrix of it exists Question number 15

Answer 1

2x2 matrix's inverse:

`\begin{gathered} A^((-1))=\begin{bmatrix}{a} & {b} & {} \\ {c} & {d} & {}\end{bmatrix}^((-1))=(1)/(ad-bc)\begin{bmatrix}{d} & {-b} & {} \\ {-c} & {a} & \end{bmatrix} \\ \\ \\ It\text{ exists only if: } \\ ad-bc\\e0 \end{gathered}`

For the given matrix:

`\begin{gathered} \begin{bmatrix}{6} & {-3} & \\ {-8} & {4} & {}\end{bmatrix} \\ \\ A^((-1))=(1)/(6*4-(-3)*(-8))\begin{bmatrix}{4} & {3} & {} \\ {8} & {6} & {}\end{bmatrix} \\ \\ A^((-1))=(1)/(24-24)\begin{bmatrix}{4} & {3} & {} \\ {8} & {6} & {}\end{bmatrix} \\ \\ A^((-1))=(1)/(0)\begin{bmatrix}{4} & {3} & {} \\ {8} & {6} & {}\end{bmatrix} \\ \\ \end{gathered}`As the determinat (ad-bc) is 0 the matrix isn't a invertible matrix. The inverse of the given matrix doesn't exist