Question

Find the characteristic polynomial of the 3x3 matrix.

Answer 1

\[\left[\begin{matrix}0 & -4 & 4 \\ 1 & 4 & -1 \\ -1& -2 & 5\end{matrix}\right]\]

Answer 2

\[Pa (λ)= | \left[\begin{matrix}λ & 0 & 0 \\ 0 & λ & 0 \\ 0 &0 &λ\end{matrix}\right]\]

Answer 3

this is unit matrix second one

Answer 4

So, you end up with \[\left[\begin{matrix}λ & -4 & 4 \\ 1 & 4-λ & -1 \\ -1 & -2& 5-λ\end{matrix}\right]\]

Answer 5

But after that I don't know what to do.

Answer 6

The λ in the first row, first column should be negative.

Answer 7

what u want to do

Answer 8

I need to find the determinant.

Answer 9

we can find it using technology i think

Answer 10

here is my answer. i hate computing these things
http://www.wolframalpha.com/input/?i=det%28 {{-x%2C+-4%2C+4}%2C+{1%2C+4-x%2C+-1}%2C+{-1%2C+-2%2C+5-x}}%29

Answer 11

I got:
\[-λ^{3}+ 9λ^{2}-26λ+24\]

Answer 12

that is what i got by cheating

Answer 13

Now if you set that = to zero. Would you get this:
\[λ= -3, \sqrt{26}, and -8/3\]