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Sliva [168]
3 years ago
8

Find the inverse of matrix [3-1-10 9]

Mathematics
1 answer:
levacccp [35]3 years ago
4 0
\mathbf A=\begin{bmatrix}3&-1\\-10&9\end{bmatrix}

The inverse is given by 

\mathbf A^{-1}=\dfrac1{\det\mathbf A}\mathrm{adj}\,\mathbf A

where \det\mathbf A is the determinant of the matrix, and \mathrm adj\,\mathbf A is the adjugate matrix, or transpose of the cofactor matrix.

\det\mathbf A=\begin{vmatrix}3&-1\\-10&9\end{vmatrix}=3(9)-(-1)(-10)=17

\mathrm{adj}\,\mathbf A=\begin{bmatrix}9&10\\1&3\end{bmatrix}^\top=\begin{bmatrix}9&1\\10&3\end{bmatrix}

So the inverse is

\mathbf A^{-1}=\dfrac1{17}\begin{bmatrix}9&1\\10&3\end{bmatrix}
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