Find the Inverse [[3,-4],[-2,7]]

Problem

[[3,−4],[−2,7]]

Solution

1. Identify the matrix A and its elements a=3 b=−4 c=−2 and d=7

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

det(A)=(3)*(7)−(−4)*(−2)

det(A)=21−8

det(A)=13

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

A(−1)=1/13*[[7,−(−4)],[−(−2),3]]

4. Simplify the signs inside the matrix.

A(−1)=1/13*[[7,4],[2,3]]

5. Distribute the scalar 1/13 to each element of the matrix.

A(−1)=[[7/13,4/13],[2/13,3/13]]

Final Answer

[[3,−4],[−2,7]](−1)=[[7/13,4/13],[2/13,3/13]]

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