Question

Find the adjoint and inverse of the matrix [1 2 ]
[3 -5 ]​

Answer 1

Answer:

see ans in the form of image.

Answer 2

The answers are   $\left[\begin{array}{cc}-5&2\\3&1\end{array}\right]$ and $\left[\begin{array}{cc}\frac{5}{11} &\frac{-2}{11} \\\frac{-3}{11}&\frac{-1}{11}\end{array}\right]$.

Given:

$\left[\begin{array}{cc}1&2\\3&-5\end{array}\right]$

To Find:

The adjoint and inverse of the matrix

Solution:

The adjoint of the matrix is given as the transverse of the cofactor matrix.

The matrix made by cofactors is $\left[\begin{array}{cc}-5&3\\2&1\end{array}\right]$.

The transverse of this matrix is $\left[\begin{array}{cc}-5&2\\3&1\end{array}\right]$.

Hence the adjoint matrix is $\left[\begin{array}{cc}-5&2\\3&1\end{array}\right]$.

The inverse of a matrix is given as the adjoint matrix divided by the determinant of the matrix.

The determinant of the matrix is given as

$1*-5-2*3=-11$

The inverse matrix is given as

$\frac{\left[\begin{array}{cc}-5&2\\3&1\end{array}\right]}{-11}=\left[\begin{array}{cc}\frac{5}{11} &\frac{-2}{11} \\\frac{-3}{11}&\frac{-1}{11}\end{array}\right]$.

Hence the inverse matrix is $\left[\begin{array}{cc}\frac{5}{11} &\frac{-2}{11} \\\frac{-3}{11}&\frac{-1}{11}\end{array}\right]$.

#SPJ2