Find $2times 2$ symmetric matrix $A$ given two eigenvalues and one eigenvector
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I am having trouble finding the symmetric matrix $A$ given eigenvalues $1$ and $4$ and eigenvector $(1, 1)$ corresponding to eigenvalue $1$ . I feel like I'd have to use the equation $A=PD(P^{-1})$ , but I'm having trouble finding the matrix $P$ if I can't find the second eigenvector. Any help is appreciated, thanks!
linear-algebra eigenvalues-eigenvectors
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edited Dec 7 '18 at 22:06
user376343
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asked Dec 7 '18 at 21:52