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  • Find the inverse of each of the matrices (if it exists). Q:5 Matrix 2 -2 4 3

Q : 5          Find the inverse of each of the matrices (if it exists).

                   \small \begin{bmatrix} 2 &-2 \\ 4 & 3 \end{bmatrix}

Answers (1)

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Given matrix :  \small \begin{bmatrix} 2 &-2 \\ 4 & 3 \end{bmatrix}

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| = (6+8) = 14

Now, calculating the cofactors terms and then adjA.

A_{11} = (-1)^{1+1} (3) = 3

A_{12} = (-1)^{1+2} (4) = -4

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

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

So, we have adjA = \begin{bmatrix} 3 &2 \\ -4& 2 \end{bmatrix}

Therefore inverse of A will be:

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

= \frac{1}{14}\begin{bmatrix} 3 &2 \\ -4& 2 \end{bmatrix} = \begin{bmatrix} \frac{3}{14} &\frac{1}{7} \\ \\ \frac{-2}{7} & \frac{1}{7} \end{bmatrix}

 

Posted by

Divya Prakash Singh

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