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Find $2times 2$ symmetric matrix $A$ given two eigenvalues and one eigenvector

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1 $begingroup$ 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 share | cite | improve this question edited Dec 7 '18 at 22:06 user376343 3,403 3 8 26 asked Dec 7 '18 at 21:52 ...