Find the Inverse [[0.60,-0.35],[-0.41,0.76]]

Problem

[[0.60,−0.35],[−0.41,0.76]]

Solution

1. Identify the matrix A and its elements a=0.60 b=−0.35 c=−0.41 and d=0.76

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

det(A)=(0.60)*(0.76)−(−0.35)*(−0.41)

det(A)=0.456−0.1435

det(A)=0.3125

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

A(−1)=1/0.3125*[[0.76,0.35],[0.41,0.60]]

4. Divide each element of the adjugate matrix by the determinant.

0.76/0.3125=2.432

0.35/0.3125=1.12

0.41/0.3125=1.312

0.60/0.3125=1.92

Final Answer

[[0.60,−0.35],[−0.41,0.76]](−1)=[[2.432,1.12],[1.312,1.92]]

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