Eigenvalues and Eigenvectors: Finding the Roots of a Matrix

[kev.thomson96]

Homework Statement

we have this matrix
6 - 1 0
-1 -1 -1
0 -1 1
We need to find it's eigenvalues and eigenvectors

Homework Equations

The Attempt at a Solution

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I wrote the characteristic equation - det(A- λxunit matrix) to find the roots and got (-λ^3)+8(λ^2)+λ-6 instead of -λ(^3)+6(λ^2)+3λ-13, which restricts me from getting the eigenvalues and vectors in the end. I don't think I'm expanding the determinant correctly, even though I know the -1 on r1, c2 turns into a +.
Do I have to apply cofactors to every row, or just to the coefficients of the 2x2 matrix determinants (6 -(-1) and 0)

These are the supposed answers

 

[Buzz Bloom]

Hi kev:

You need to calculate the determinant as the sum of six products, each with an appropriate +/- sign. Each product includes one element from each row and each column.

See https://en.wikipedia.org/wiki/Determinant .

Also, you may have forgotten that the cells along the main diagonal all have a "-λ" added to the numerical value in the cell.

Hope this helps.

Regards,
Buzz