1. ## Linear Algebra..

We were given a 3 x 3 matrix,
1 2 0
-1 -1 1
0 1 1

a) the characteristic polynomial of A.
b) eigenvalues of A.
c) the basis for each eigenspace of A.
d) the algebraic and geometric multiplicity of each eigenvalue.

I don't know what I did wrong for a & b

a) I did the crossproduct and got -3L^3 + L^2 + L - 1 (-L^3 + L^2)
b) L = 1,1 (L=0,1)
c) I know how to get this, but I need the right eigenvalues...
d) I have no idea what this means, could someone explain?

2. Use $Det(M-\lambda I)$ and find the determinant.

The first bit is like this:

$\begin{vmatrix}
{1-\lambda}&{2}&{0}\\
{-1}&{-1-\lambda}&{1}\\
{0}&{1}&{1-\lambda}
\end{vmatrix}$

The expression obtained form this is the characteristic equation.

Solving this (ie. find when the determinant=0) will give you the eigenvalues.