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## Homework Statement

Consider the following matrix

*A*(whose 2nd and 3rd rows are not given), and vector

**x**.

*A*=

4 4 2

* * *

* * *

**x**=

2

-1

10

Given that

**x**is an eigenvector of the matrix

*A*, what is the corresponding eigenvalue?

## Homework Equations

## The Attempt at a Solution

4−λ 4 2

a b−λ c

d e f−λ=

det (λI

_{3}-3) =

−λ

^{3}+b+f+4×λ

^{2}+4×a−4×b+2×d+c×e−b×f−4×f×λ+−2×b×d+4×c×d+2×a×e−4×c×e−4×a×f+4×b×f

Don't know if I'm on the right track. Trying to find the roots of this characteristic equation, but there's so many unknowns.