Eigenvector, Eigenvalue and diagonalising help

Hi guys, i've got some issues at the moment regarding eigenvector and eigenvalue Your help will be greatly appreciated. Thanks =)

First the matrix c is given as:

3 1 0

2 2 0

1 6 5 (Note: i have shown that the eigenvalues are 1,4 and 5).

It then asked me to write out the polynomial of C, namely write out: determinant(C - lamda multiply the identity matrix) as a polynomial of lamda. Any ideas whats this about?

Lastly, there are 4 column vectors:

a:

3

2

-4

b:

-6

-4

8

c:

0

-5

0

d:

0

0

-5

The sets {ac}, {ad}, {bc},d}, {bd}, and {cd} are all linearly independent.

The question asked me to find a basis of the vector space R^3 which lies in {a b c d}

any ideas guys?

thanks. Your help is much appreciated.