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9 votes
Determine whether the following matrices are inverse matrices of one another


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How to do this please help​

User Brynn
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1 Answer

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14 votes

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Answer:

they are not

Explanation:

The inverse matrix is the transpose of the cofactor matrix, divided by the determinant.

The cofactor matrix for a 2×2 matrix is ...


image

The transpose of this will have the off-diagonal terms swapped, so the inverse matrix is ...


image

We see that the second matrix is the transpose of the cofactor matrix, but the determinant is (5)(2)-(3)(4) = -2, so there has clearly been no division by the determinant. The actual inverse matrix of the first one shown is ...


image

_____

You can compute the matrix product to see if you get an identity matrix. Here, the upper left term in the product is ...

(5)(2) +(4)(-3) = -2 . . . . . not 1, so the product matrix is not an identity matrix

The matrices are not inverses.

User Cclloyd
by
2.7k points
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