I am little confused about the choice of eigenvectors chosen by my book. I am wondering if an eigenvalue can have multiple eigenvectors and if all are equally correct. Case in point the example below:(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

find a fundamental matrix for the system x'(t) = Ax(t) for the given matrix A:

A = Row1 = {3 1 -1}

Row2 = {1 3 -1}

Row3 = {3 3 -1}

The attempt at a solution:

So i go through the motions and find that th eigenvalues are 1 and -2. the eigenvector for eValue 1 = {1, 1, 3}

When I try to solve for the eVector for eValue =2, There are 2 possibilties because:

(A-rI), where r = 2:

Row1 = {1 1 -1}

Row2 = {1 1 -1}

Row3 = {3 3 -3}

which basically leads to the equation U1 + U2 - U3 = 0

i.e. U3 = U1 + U2

from here, I can say

U1 = s, U2 =t, and U3 = s + t, leading to the eVectors:

{s, t, s+t}

or s * {1,0,1} + t * {0,1,1}

OR i can say U1 = -U2 + U3, U2 =t, U3 =s and my eVectors are:

{t - s, t, s} or t*{1, 1, 0} + s*{-1, 0, 1}

Which is correct? the book says the 2nd one but i dont see why pick one over the other.

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# Homework Help: [Lin Alg - Eigenvectors]

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