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

Problem

[[4,7],[1,2]](−1)

Solution

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

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

det(A)=(4)*(2)−(7)*(1)

det(A)=8−7

det(A)=1

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

A(−1)=1/1*[[2,−7],[−1,4]]

4. Simplify the resulting matrix by multiplying each element by the scalar 1/1

A(−1)=[[2,−7],[−1,4]]

Final Answer

[[4,7],[1,2]](−1)=[[2,−7],[−1,4]]

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