I have this matrix: $$\begin{bmatrix}6&-2&2\\-2&3&b\\2&b&a\end{bmatrix}$$
which has: $$\begin{bmatrix}1\\0\\-2\end{bmatrix}$$ as an eigen vector.
what is the shortest path to find a & b and all eigen values and other eigen vectors
2026-03-29 11:43:37.1774784617
what is the shortest path to solve a matrix with unknown elements and an eigenvector?
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Use the fundamental definition of an eigenvector of the matrix $A$: it’s a nonzero vector $\mathbf v$ such that $A\mathbf v=\lambda\mathbf v$ for some scalar $\lambda$. Plug the given matrix and vector into this equation and you will get a system of equations for $a$, $b$ and $\lambda$.