- #1
erok81
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Homework Statement
This is a simple example from the book, but it gets the point across nicely.
In this problem eigenanalysis is used as a method to solve linear systems.
The matrix...
[4 2]
[3 -1]
Eigenvalues are -2, 5.
Homework Equations
[tex](A-\lambda I)v=0[/tex]
x'=[above matrix]x
The Attempt at a Solution
So I solve for the eigenvector using the first case, [tex]\lambda=-2[/tex]
New matrix with above eigenvalue:
[6 2]
[3 1]
The book gives the eigenvector as [1,-3]^T
I get [-1/3,1]^T
From my rref of:
[3 1]
[0 0]
My vector and the books vector are off by a value of -3. Which I think is because I tried the rref and they just used two equations with the two unknowns and "guessed' values.
I ran into this problem a few times in the homework as well, which would eventually lead to an incorrect answer compared to the textbook.
My question is, why do you solve a normal matrix using the rref but it seems you can't do the same with eigenanalysis? Do I just break them into equations and guess solutions?
Everyone I did in the homework I ended up with the same type of answer - off by some value that I can see used to be in the matrix like the above example.