- #1

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**Homework Statement**

[PLAIN]http://img14.imageshack.us/img14/7826/70745131.jpg [Broken]

**The attempt at a solution**

How do I go about solving this problem?

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- Thread starter temaire
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- #1

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[PLAIN]http://img14.imageshack.us/img14/7826/70745131.jpg [Broken]

How do I go about solving this problem?

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- #2

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2..

is dis correct!

is dis correct!

- #3

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2..

is dis correct!

????

- #4

Mark44

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Maybe, maybe not.

- #5

Mark44

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What does it mean to say that a number lambda is an eigenvalue of a matrix?

- #6

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it means that no. is the eigen value of new matrix formed by the expression..

A^2010 -2A+3I

A^2010 -2A+3I

- #7

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- #8

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How did you show it was 2?

- #9

Mark44

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You didn't answer my question. Here's a slightly different question. What does it mean to say that 3 is an eigenvalue of a matrix A?it means that no. is the eigen value of new matrix formed by the expression..

A^2010 -2A+3I

- #10

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this value...(e-value) is a factor by which matrix changes the length of vector...

- #11

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You didn't answer my question. Here's a slightly different question. What does it mean to say that 3 is an eigenvalue of a matrix A?

hope this give answer to your question!

- #12

Mark44

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I'm looking for an equation that involves A and 3.

- #13

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- #14

Mark44

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With your problem, you know that 1 is an eigenvalue of A, so A

(A

- #15

Mark44

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Think about the other problem you posted. If Ax = 1x, what are A^{2}**x**, A^{3}**x**, A^{4}**x**, ...?

- #16

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All would be 1x

- #17

Mark44

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OK, so what would (A^{2010} - 2A + 3I)**x** be?

- #18

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Also 1x

- #19

Mark44

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No it isn't.Also 1x

- #20

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No it isn't.

Whoops lol, I meant 2.

- #21

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So would it be enough to say that since A=1, A^2010 - 2A + 3I = 1 -2 + 3 = 2?

- #22

Mark44

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No, A is a matrix, so it can't be equal to any number, and A^2010 - 2A + 3I [itex]\neq[/itex] 2So would it be enough to say that since A=1, A^2010 - 2A + 3I = 1 -2 + 3 = 2?

However, you know that A

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