# characheristic equation

• Nov 29th 2007, 07:29 PM
Darren mcarty
characheristic equation
1)find the eigenvalues for the matrix
A = 1 2 1
0 3 1
0 5 -1
B) for each eigenvalue found above find a basis for the eigenspace

C)join all basis vectors from B) into a single set. does this set form a basis R^3? why or why not?

D)use C to express the v= [4 2 8] as a linear combination of eigenvectors. then find A15 v without having to work too hard.

2) repeat a-c for the matrix
B= 1 5 1
0 3 -1
0 1 1
• Nov 29th 2007, 07:38 PM
kalagota
Quote:

Originally Posted by Darren mcarty
1)find the eigenvalues for the matrix
A = 1 2 1
0 3 1
0 5 -1
B) for each eigenvalue found above find a basis for the eigenspace

C)join all basis vectors from B) into a single set. does this set form a basis R^3? why or why not?

D)use C to express the v= [4 2 8] as a linear combination of eigenvectors. then find A15 v without having to work too hard.

2) repeat a-c for the matrix
B= 1 5 1
0 3 -1
0 1 1

have you tried solving the characteristic polynomial $|xI - A|$? what was that?
• Nov 29th 2007, 08:37 PM
Darren mcarty
yes but i didnt know where to go after subtracting the lamda
• Nov 29th 2007, 08:55 PM
kalagota
Quote:

Originally Posted by Darren mcarty
yes but i didnt know where to go after subtracting the lamda

try factoring your char. poly.. ie, $P_A (x) = (x-k_1)(x-k_2)...$
what was your char.poly and also the factored form?

i got, $P_A (x) = (x-1)(x-4)(x+2)$
so the eigenvalues are 1,4,-2..
• Nov 29th 2007, 09:02 PM
Darren mcarty
i did not get those ... but thanks at least i have something to work towards