Find the Inverse 5A=[[5,1],[32,6]]

Problem

5*A=[[5,1],[32,6]]

Solution

1. Identify the matrix M=5*A and its elements a=5 b=1 c=32 and d=6

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

det(M)=(5)*(6)−(1)*(32)

det(M)=30−32

det(M)=−2

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

(5*A)(−1)=1/(−2)*[[6,−1],[−32,5]]

4. Distribute the scalar −1/2 to each element inside the matrix.

(5*A)(−1)=[[6/(−2),(−1)/(−2)],[(−32)/(−2),5/(−2)]]

5. Simplify the resulting fractions to find the final inverse matrix.

(5*A)(−1)=[[−3,0.5],[16,−2.5]]

Final Answer

(5*A)(−1)=[[−3,1/2],[16,−5/2]]

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