Question

Question about eigenvectors and eigenvalues.

Answer 1

So I set up:

A*u=λ*u

I don't know how to solve for λ though :/ .

Answer 2

I literally just learnt this thing so if I am doing something wrong please tell me.

Answer 3

Okay, first just multiply \(A\;\mathbf{u}\) right out.

Answer 4

Eww...

Answer 5

Kk. 1 sec.

Answer 6

You'll only need to find the first row, fortunately.

Answer 7

So the first row should be -6 7 and 0 I believe? Or did I screw up my multiplication?

Answer 8

Suppose \(A\; \mathbf{u}=\mathbf{v}\) \[
\lambda \cdot u_1= v_1 \implies \lambda \cdot -6 = v_1
\]

Answer 9

You have to multiply \(A\) and \(\mathbf{u}\) using matrix multiplication.

Answer 10

Yep I got that.

Answer 11

So the first row is 1. The second row is -6a+7b+2c and the third row is -6a+7e+2f .

Answer 12

so can I say λ=-1/6 then?

Answer 13

So you know that: \[
\lambda \cdot -6 = 1
\]You can solve for the eigen value now.

Answer 14

So λ = -1/6 right?

Answer 15

Yeah.

Answer 16

Thanks a lot!