SOLUTION: I have worked out Eigenvalues of the following matrix 1 -1 2 0 2 0 3 -3 2 They are = -1, 2, 4 I cant seem to work out the eigenvector for -1. Could someone show me step

Question 361049: I have worked out Eigenvalues of the following matrix
1 -1 2
0 2 0
3 -3 2
They are = -1, 2, 4
I cant seem to work out the eigenvector for -1. Could someone show me step by step how this achieved. I can then use this to work out 2, and 4.

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
For λ = -1, replacing -1 into the homogeneous system A - λI = O, we get the augmented homogeneous system
.
~Divide r2 and r3 by 3.
~Add row2 to r3
~-2*r3 + r1
~Add r2 to r1
~Interchange r1 and r3.
Thus y = 0 and x + z = 0, or z = -x. hence,
. The basis for eigenspace for λ = -1 is then , and this is its eigenvector.
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