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3 $begingroup$ The matrix $A in M_3(mathbb{R})$ satisfy $A^t=A$ and $(1,2,1), (-1,1,0)$ are eigenvectors of $A$ . Which vector is also an eigenvector of $A$ ? Alternatives: $(0,0,1)$ ; $(1,1,-3)$ ; $(1,1,3)$ ; There is no other eigenvector . The problem with this exercise is that I don't know the matrix $A$ , and I don't have any eigenvalue to start with. I can get a matrix with less variables using $A = A^t$ , but there's still 6 variables. Any tips or guidance is appreciated. linear-algebra eigenvalues-eigenvectors share | cite | improve this question asked 1 hour ago rodorgas rodorgas