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]
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