Eigenvalues and eigenvectors

  • Thread starter Angello90
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  • #1
Angello90
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Hey guys,

I'm studing to my exams now, and I came accors this question i eigenvectors where you find them and bla bla. There is part to it which asks to express vetor

X= [2/1]

as a linear combination of eigenvectors. Hence calculate B2X, B3X, B4X and B51X, simplifying your answers as much as possible.

How do you do the linear combination?

Thanks!
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
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The "bla bla" does not help at all. Perhaps you could post the entire question?

For example, what does "[2/1]" mean? Is that a two dimensional vector with components 2 and 1? Write it as a linear combination of what eigenvectors? Is there some matrix or linear transformation you haven't mentioned? And what are " B2X, B3X, B4X and B51X"? Those are not standardized notations.
 
  • #3
Angello90
65
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Ok sorry I suppose I didn't make myself clear.

I have two eigenvectors.

First: Look at 1.jpg
Second : Look at 2.jpg

The vector X (look at 3.jpg) is to be written as a linear combination of eigenvectors. How do you do that? It's just a theory I'm interested in not solution to the question.

Thanks and sorry for inconvenience.
 

Attachments

  • 1.jpg
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  • 2.jpg
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  • 3.jpg
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  • #4
jrlaguna
107
1
OK, now your question is clear. Let v1=(-3,1) be the first eigenvector, and v2=(-2,1) the second one. Now you want "a1" and "a2" such that

X = a1 v1 + a2 b2

That is equivalent to solving a linear system

[2] = [-3 -2] [a1]
[1] [ 1 1] [a2]

Where the eigenvectors went as columns.
 
  • #5
Angello90
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So the answer should look like this (look at the ans.jpg)?
And are a1 and a2 variables?

Thanks a lot!
 

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  • #6
jrlaguna
107
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correct! :)
 
  • #7
Angello90
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Thanks a lot jrlaguna!
 

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