Question

Eigenvalue matrix question,

If the determinant is zero
find values for λ?

Answer 1

I dont really see how knowing the determinant is 0 helps. That lets us know at least one of the eigenvalues is 0 (since the determinant of a matrix is the product of its eigenvalues), but we dont know if only one is 0, or they all are 0, or whatever. We have to get out hands dirty and calculate:\[\det(A-\lambda I)\]

Answer 2

The answers are
λ1 = -1+j
λ2 = -1-j
λ3 = -2
λ4 = -3

Answer 3

then the determinant of that matrix cant be zero.

Answer 4

i dont understand the matrix itself, if i substract the lambda matrix from the other, i get a bigger matrix.

exactly ;)

Answer 5

Since the matrix is in a nice form, this isnt as bad of a problem as it could be. Its a 4x4 with 2x2 sub matrices. So we can just look at the 2x2's instead.

Answer 6

I just comes down to being able to create that characteristic equation. is that what you are having trouble with?

Answer 7

it*

Answer 8

if the determinant is 0, then one of the eigenvalues must be 0, because the product of the eigenvalues = determinant

Answer 9

right, thats why the determinant of this matrix cant be 0.

Answer 10

hiii joemath

so what you did is you solved the matrix with the block matrix theorem

Answer 11

right, in this special case, we can just look at the 2x2 blocks individually instead of the whole 4x4 matrix. it makes getting determinants easier.

Answer 12

yeahh... it certainly is! i thought... i have to reduce the substracted matrix, with only the diagonal element.. but that was a lot of work and i dont got the final answer..

the block matrix is the best option :) thank you joemath :)