Find the Inverse [[1,3],[5,7]]

Problem

[[1,3],[5,7]]

Solution

1. Identify the matrix A and its elements a=1 b=3 c=5 and d=7

2. Calculate the determinant using the formula det(A)=a*d−b*c

det(A)=(1)*(7)−(3)*(5)

det(A)=7−15

det(A)=−8

3. Apply the inverse formula for a 2×2 matrix, which is A(−1)=1/det(A)*[[d,−b],[−c,a]]

A(−1)=1/(−8)*[[7,−3],[−5,1]]

4. Distribute the scalar 1/(−8) to each element in the matrix.

A(−1)=[[−7/8,3/8],[5/8,−1/8]]

Final Answer

[[1,3],[5,7]](−1)=[[−7/8,3/8],[5/8,−1/8]]

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