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A=[ −3
−8

8
2

], then det hus, A^−1
=

User Dasunx
by
8.5k points

1 Answer

1 vote

Answer:

To find the determinant of matrix A, we can use the formula for a 2x2 matrix:

det(A) = (a*d) - (b*c)

In this case, we have:

A = [ -3 8

-8 2 ]

Using the formula, we can calculate the determinant as:

det(A) = (-3 * 2) - (8 * -8)

= -6 - (-64)

= -6 + 64

= 58

Now, to find the inverse of matrix A, we can use the formula:

A^-1 = (1/det(A)) * adj(A)

Where adj(A) is the adjugate of matrix A.

The adjugate of matrix A can be found by swapping the diagonal elements and changing the sign of the off-diagonal elements:

adj(A) = [ 2 -8

8 -3 ]

Now, we can find the inverse of A:

A^-1 = (1/58) * [ 2 -8

8 -3 ]

Multiplying each element by 1/58, we get:

A^-1 = [ 2/58 -8/58

8/58 -3/58 ]

Simplifying the fractions, we have:

A^-1 = [ 1/29 -4/29

4/29 -1/29 ]

Therefore, the inverse of matrix A, A^-1, is:

A^-1 = [ 1/29 -4/29

4/29 -1/29 ]

Explanation:

User Misteryes
by
7.8k points

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