Find the Eigenvalues inverse ([[1,2,3],[4,5,6],[7,8,9]])

Problem

Eigenvalues*([[1,2,3],[4,5,6],[7,8,9]](−1))

Solution

1. Identify the matrix A and its properties.

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

2. Calculate the determinant of A to determine if the inverse exists.

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

3. Simplify the determinant calculation.

det(A)=1*(45−48)−2*(36−42)+3*(32−35)

4. Evaluate the final sum for the determinant.

det(A)=−3+12−9=0

5. Conclude that since the determinant is zero, the matrix A is singular (non-invertible).

det(A)=0

6. Determine the status of the eigenvalues of the inverse. Because the matrix has no inverse, the eigenvalues of the inverse are undefined.

Inverse does not exist

Final Answer

Eigenvalues*([[1,2,3],[4,5,6],[7,8,9]](−1))=Undefined (Matrix is singular)

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