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Does the given matrix, A, have an inverse? If it does, what is A-1?
5
12
A
=
2
5

Does The Given Matrix A Have An Inverse If It Does What Is A1 5 12 A 2 5 class=

Sagot :

Abidemiokinidn

The inverse of the function is [tex]\left[\begin{array}{ccc}5&-12\\-2&5\\\end{array}\right][/tex]

Inverse of a matrix

For a 2 by 2 matrix, the inverse is generally expressed as:

[tex]\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] ^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right][/tex]

Since the given matrix is a square matrix and 2 by 2, therefore it will have an inverse.

Determine the determinant

|A| = 5(5) - 2(12)

|A| = 25 - 24

|A| = 1

Substitute the values into the formula above

[tex]\left[\begin{array}{ccc}5&12\\2&5\\\end{array}\right] ^{-1}=(1)\left[\begin{array}{ccc}5&-12\\-2&5\\\end{array}\right][/tex]

Hence the inverse of the function is [tex]\left[\begin{array}{ccc}5&-12\\-2&5\\\end{array}\right][/tex]

Learn more on inverse of a matrix here: https://brainly.com/question/27924478

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