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

Problem

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

Solution

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

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

det(A)=(1)*(2)−(7)*(4)

det(A)=2−28

det(A)=−26

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

A(−1)=1/(−26)*[[2,−7],[−4,1]]

4. Distribute the scalar 1/(−26) to each element inside the matrix.

A(−1)=[[2/(−26),(−7)/(−26)],[(−4)/(−26),1/(−26)]]

5. Simplify the fractions to their lowest terms.

A(−1)=[[−1/13,7/26],[2/13,−1/26]]

Final Answer

[[1,7],[4,2]](−1)=[[−1/13,7/26],[2/13,−1/26]]

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