Find the Inverse [[3,7],[8,4]]

Problem

[[3,7],[8,4]]

Solution

1. Identify the matrix A and its elements a=3 b=7 c=8 and d=4

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

det(A)=(3)*(4)−(7)*(8)

det(A)=12−56

det(A)=−44

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

A(−1)=1/(−44)*[[4,−7],[−8,3]]

4. Distribute the scalar 1/(−44) to each element inside the matrix.

A(−1)=[[4/(−44),(−7)/(−44)],[(−8)/(−44),3/(−44)]]

5. Simplify the fractions to their lowest terms.

A(−1)=[[−1/11,7/44],[2/11,−3/44]]

Final Answer

[[3,7],[8,4]](−1)=[[−1/11,7/44],[2/11,−3/44]]

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