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  • Find the inverse of each of the matrices (if it exists). Q: 6 Matrix -1 5 -3 2

Q : 6         Find the inverse of each of the matrices (if it exists).

                 \small \begin{bmatrix} -1 &5 \\ -3 &2 \end{bmatrix}

Answers (1)

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Given the matrix :  \small \begin{bmatrix} -1 &5 \\ -3 &2 \end{bmatrix} = A

To find the inverse we have to first find adjA then as we know the relation:

A^{-1} = \frac{1}{|A|}adjA

So, calculating |A| :

|A| = (-2+15) = 13

Now, calculating the cofactors terms and then adjA.

A_{11} = (-1)^{1+1} (2) = 2

A_{12} = (-1)^{1+2} (-3) = 3

A_{21} = (-1)^{2+1} (5) =-5

A_{22} = (-1)^{2+2} (-1) = -1

So, we have adjA = \begin{bmatrix} 2 &-5 \\ 3& -1 \end{bmatrix}

Therefore inverse of A will be:

A^{-1} = \frac{1}{|A|}adjA

= \frac{1}{13}\begin{bmatrix} 2 &-5 \\ 3& -1 \end{bmatrix} = \begin{bmatrix} \frac{2}{13} &\frac{-5}{13} \\ \\ \frac{3}{13} & \frac{-1}{13} \end{bmatrix}

Posted by

Divya Prakash Singh

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