Find the Inverse [[0.6,-0.4],[0.8,-0.2]]

Problem

[[0.6,−0.4],[0.8,−0.2]]

Solution

1. Identify the matrix A and its elements a=0.6 b=−0.4 c=0.8 and d=−0.2

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

det(A)=(0.6)*(−0.2)−(−0.4)*(0.8)

det(A)=−0.12−(−0.32)

det(A)=0.2

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

A(−1)=1/0.2*[[−0.2,0.4],[−0.8,0.6]]

4. Multiply by the scalar 1/0.2 which is equivalent to multiplying by 5

A(−1)=[[5*(−0.2),5*(0.4)],[5*(−0.8),5*(0.6)]]

A(−1)=[[−1,2],[−4,3]]

Final Answer

[[0.6,−0.4],[0.8,−0.2]](−1)=[[−1,2],[−4,3]]

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