Find the Inverse [[3,-9],[-2,5]]

Problem

[[3,−9],[−2,5]]

Solution

1. Identify the matrix A and its elements a,b,c,d for the formula of a 2×2 inverse.

A=[[a,b],[c,d]]=[[3,−9],[−2,5]]

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

det(A)=(3)*(5)−(−9)*(−2)

det(A)=15−18

det(A)=−3

3. Apply the inverse formula A(−1)=1/det(A)*[[d,−b],[−c,a]]

A(−1)=1/(−3)*[[5,9],[2,3]]

4. Distribute the scalar factor −1/3 to each element in the matrix.

A(−1)=[[−5/3,−3],[−2/3,−1]]

Final Answer

[[3,−9],[−2,5]](−1)=[[−5/3,−3],[−2/3,−1]]

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