Question

Hi i need help regarding vector. if Av1=-12v1,v1 is non-zero vector. Av2=-9v2,v2 is non-zero vector. Av3=0v3,v3 is non-zero vector. A is a 3 by 3 matrix.
Let P = (v1,v3,v2)
And AP = P <0 d 0> <0 0 e>. Find the value of e.

Answer 1

as an aside, notice your vectors v1, v2 and v3 are eigenvectors and the contents -12,-9 and 0 are their corresponding eigenvalues.

your c, d, and e are also the eigenvalues.

Answer 2

@phi P is the matrix of eigenvectors which diagonalize A, right?

Answer 3

Yes,
A= P L P^-1 where L is the diagonal matrix of eigenvalues

Answer 4

so, e =-9, that's it, right?

Answer 5

oh, no, I see my mistake

Answer 6

yes, if you want L, you do what you posted.

e is the eigenvalue for v2, so e=-9, yes