- #1
eherrtelle59
- 25
- 0
Ok, this is starting to come back to me, but I'm stuck again
M=\begin{bmatrix}
(1-\frac{4}{3}) & 0 \\
-\frac{c}{3} & -c \\
\end{bmatrix}
Find eigenvectors and eigenvalues.
Eigenvalues are [itex] λ_1= (1-\frac{4}{3})>0[/itex] and [itex] λ_2=-c>0 [/itex]
Eigenvector for [itex] λ_2 [/itex] is <0 1>
For [itex]λ_1[/itex], I should get [itex]<(\frac{c}{3}-1) (\frac{4}{3})> [/itex]
However, I end up with (without writing out the matrix again, just giving the equation mind you)
[itex] -c*e_2 = e_1 - \frac{4}{3}*e_1 +\frac{c}{3}*e_1 [/itex]
This is [itex] -c*e_2 = (1-c)*e_1 [/itex]which gets an eigenvector of something like <(1-c) c>
Anyone see my error? Thanks
Homework Statement
M=\begin{bmatrix}
(1-\frac{4}{3}) & 0 \\
-\frac{c}{3} & -c \\
\end{bmatrix}
Find eigenvectors and eigenvalues.
Homework Equations
The Attempt at a Solution
Eigenvalues are [itex] λ_1= (1-\frac{4}{3})>0[/itex] and [itex] λ_2=-c>0 [/itex]
Eigenvector for [itex] λ_2 [/itex] is <0 1>
For [itex]λ_1[/itex], I should get [itex]<(\frac{c}{3}-1) (\frac{4}{3})> [/itex]
However, I end up with (without writing out the matrix again, just giving the equation mind you)
[itex] -c*e_2 = e_1 - \frac{4}{3}*e_1 +\frac{c}{3}*e_1 [/itex]
This is [itex] -c*e_2 = (1-c)*e_1 [/itex]which gets an eigenvector of something like <(1-c) c>
Anyone see my error? Thanks