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Algebra
Question

#7: Consider the following matrix $$A$$ (whose $$2$$ nd and $$3$$ rd rows are not given), and vector $$x$$ .

$$A = \left[ \begin{array} { c c c } { 1 } & { - 4 } & { - 9 } \\ { * } & { * } & { * } \\ { * } & { * } & { * } \end{array} \right] , x = \left[ \begin{array} { c } { 2 } \\ { 8 } \\ { 10 } \end{array} \right]$$

Given that $$x$$ is an eigenvector of the matrix $$A$$ , what is the corresponding eigenvalue?

Answer

$$Ax= \lambda x\Rightarrow 2- 32- 90= 2\lambda\Rightarrow \lambda = -60$$

Solution
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