Find the Inverse [[34,64],[7,13]]

Problem

[[34,64],[7,13]]

Solution

1. Identify the matrix A and its elements a=34 b=64 c=7 and d=13

A=[[34,64],[7,13]]

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

det(A)=(34)*(13)−(64)*(7)

det(A)=442−448

det(A)=−6

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

A(−1)=1/(−6)*[[13,−64],[−7,34]]

4. Distribute the scalar 1/(−6) to each element in the matrix.

A(−1)=[[−13/6,64/6],[7/6,−34/6]]

5. Simplify the fractions where possible.

A(−1)=[[−13/6,32/3],[7/6,−17/3]]

Final Answer

[[34,64],[7,13]](−1)=[[−13/6,32/3],[7/6,−17/3]]

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