Find the Inverse [[1,2,3],[4,5,6],[7,8,9]]

Problem

[[1,2,3],[4,5,6],[7,8,9]]

Solution

1. Identify the matrix A and its elements.

A=[[1,2,3],[4,5,6],[7,8,9]]

2. Calculate the determinant of the matrix using the first row expansion.

det(A)=1*(5⋅9−6⋅8)−2*(4⋅9−6⋅7)+3*(4⋅8−5⋅7)

3. Simplify the terms inside the determinant calculation.

det(A)=1*(45−48)−2*(36−42)+3*(32−35)

4. Evaluate the final value of the determinant.

det(A)=1*(−3)−2*(−6)+3*(−3)

det(A)=−3+12−9

det(A)=0

5. Conclude the existence of the inverse based on the determinant.

det(A)=0⇒The matrix is singular.

Final Answer

[[1,2,3],[4,5,6],[7,8,9]](−1)=Does not exist (Matrix is singular)

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