- #1
M55ikael
- 17
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Homework Statement
Hi! I have this frustrating equation I can't solve even though I have the answer.
I'm trying to make two Eigenvectors for my matrix. I have found λ1 and λ2, but I can't solve the resulting equations.
Homework Equations
[itex]A = \begin{bmatrix} 2 & 1 \\ -\frac{1}{2} & 1 \end{bmatrix}[/itex]
λ1= 3/2 + j/2 , λ2= 3/2 - j/2
[itex]\begin{bmatrix} 2 -(3/2 + j/2) & 1 \\ -\frac{1}{2} & 1 - (3/2 + j/2) \end{bmatrix}[/itex] * E1 = 0
Attempt at solution:
E1
α(-1-j) + 2β = 0
-α + β(-1-j) = 0
E2
α(-1+j) + 2β = 0
-α + β(-1+j) = 0
I can't make any sense out of those equations though.
Answers should be
[itex]E1 = \begin{bmatrix} 2 \\ -1+j \end{bmatrix}[/itex] * c
[itex]E2 = \begin{bmatrix} 2 \\ -1-j \end{bmatrix}[/itex] * t
c and t are different from 0
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