Find the Inverse [[1,4],[2,7]]

Problem

[[1,4],[2,7]]

Solution

1. Identify the matrix A and the formula for the inverse of a 2×2 matrix.

A=[[a,b],[c,d]]=[[1,4],[2,7]]

A(−1)=1/(a*d−b*c)*[[d,−b],[−c,a]]

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

det(A)=(1)*(7)−(4)*(2)

det(A)=7−8

det(A)=−1

3. Apply the inverse formula by swapping the elements on the main diagonal and changing the signs of the elements on the off-diagonal.

A(−1)=1/(−1)*[[7,−4],[−2,1]]

4. Distribute the scalar factor into the matrix to find the final result.

A(−1)=[[−7,4],[2,−1]]

Final Answer

[[1,4],[2,7]](−1)=[[−7,4],[2,−1]]

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