Question

Given A- 2 2 1 3 what is A-¹?

Answer 1

The inverse of matrix A = $\left[\begin{array}{cc}2&2&1&3\\\end{array}\right]$ is $A^{-1} = \frac{1}{4}$ $\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|$      

The given matrix is A = $\left[\begin{array}{cc}2&2&1&3\\\end{array}\right]$

The inverse of a matrix is given by

$A^{-1} = \frac{1}{|A|} adjA$                   ...(1)

Now, determinant of matrix A is

|A| = $\left|\begin{array}{cc}2&2&1&3\\\end{array}\right|$

= (3)(2) - (2)(1)

= 6 - 2

= 4

Now, adjoint A will be

$A_{11}$ = 3

$A_{12}$ = -1

$A_{21}$ = -2

$A_{22}$ = 2

AdjA = $\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|$

Now, substituting the values of |A| and AdjA in equation (1), we get

$A^{-1} = \frac{1}{4}$ $\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|$        

Therefore, $A^{-1} = \frac{1}{4}$ $\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|$      

Know more about Inverse of Matrix: -brainly.com/question/12442362

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