Let A = {9.6667, -8.3333; -8.6667, 83333; 0, 0, -2.0000]. Select all of the foll

Question

Let A = {9.6667, -8.3333; -8.6667, 83333; 0, 0, -2.0000]. Select all of the following vector that are excluded from eigenspace associated with eigenvector lambda = -2 . By this, I mean that the vector is entirely contained within a different vector space that does not overlap in any way with the eignenspace in question. Think about this carefully because this problem DOES test your understanding of vector spaces! Matlab can help here if you use it properly. x = [-5;5;0] x = [1;-1;0] x = [0;1;3] x=[1;2;3] x=[0;1;-1] x=[1;-2;2]

Explanation / Answer

the eigen value (-2) is an eigen value to A with multiplicity 2

and the only other eigen value is 3, which has multiplicity (1)...

so the only vector that is not contained in the eigen space (-2) is the eigen vector corresponding to 3

that is (1,-1,0) is the answer..... since it is not contained in the eigen space (-2) ......

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