Find the Inverse [[6,2],[5,7]]

Problem

[[6,2],[5,7]]

Solution

1. Identify the matrix A and its elements a=6 b=2 c=5 and d=7

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

det(A)=(6)*(7)−(2)*(5)

det(A)=42−10

det(A)=32

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

A(−1)=1/32*[[7,−2],[−5,6]]

4. Distribute the scalar 1/32 to each element inside the matrix.

A(−1)=[[7/32,(−2)/32],[(−5)/32,6/32]]

5. Simplify the fractions within the matrix where possible.

A(−1)=[[7/32,−1/16],[−5/32,3/16]]

Final Answer

[[6,2],[5,7]](−1)=[[7/32,−1/16],[−5/32,3/16]]

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