Question

Eigenvector & Eigenvalue Question

Answer 1

I solved for the eigenvalues of the general matrix (and I got 3,-3, and 2) but how do I find the eigenvalues of the given eigenvectors? @sillybilly123

Answer 2

is this cal lol

Answer 3

doing it back to front (!!) but to reverse engineer, the test is that \(M \mathbf v = \lambda \mathbf v\)

so taking your first one:

\[\left[\begin{matrix}3 & 0 & 0 \\ -3 & 0 & 2 \\ -1 & -1 -3\end{matrix}\right]\left(\begin{matrix}0 \\ -1 \\ 1\end{matrix}\right) = \lambda \left(\begin{matrix}0 \\ -1 \\ 1\end{matrix}\right) \implies \lambda = - 2\]


multiply it out

Answer 4

so

0 = 0

2 = - lambda

- 2 = lambda

Answer 5

thank you, let me try the arithmetic

Answer 6

https://www.wolframalpha.com/input/?i=eigenvalues+((3,0,0),(-3,0,2),(-1,-1,-3))

looks good per MW

Answer 7

got em, thank you ^^

Answer 8

jwd

Answer 9

shoulda said, when you move onto diagonalisation, MW gives you the full suite: eigenvalues/vectors and the rest:

https://www.wolframalpha.com/input/?i=diagonalise+((3,0,0),(-3,0,2),(-1,-1,-3))

when you understand what this stuff means/ allows you to do, you shouldn't be wasting time on crunching the numbers.