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**Unformatted text preview: **1 / √ 2-1 / √ 2 , 1 / √ 2 1 / √ 2 , 1 / √ 2 1 / √ 2 3. (3 pts) Suppose that ~v is an eigenvector of some matrix A with eigen-value λ . Suppose also that A~v is orthogonal to ~v . What can you say about λ ? We have that A~v = λ~v , and that h A~v,~v i = 0. Putting these together, we get that 0 = h A~v,~v i = h λ~v,~v i = λ h ~v,~v i Now, since ~v is an eigenvector, it is nonzero, so its length is nonzero. Above, we showed that λ times the length squared is zero, so λ must be zero....

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