How do I find the eigenvalue given unknown rows & eigen vect

  • #1
22
0

Homework Statement


Consider the following matrix A (whose 2nd and 3rd rows are not given), and vector x.

A =
4 4 2
* * *
* * *
x =
2
-1
10

Given that x is an eigenvector of the matrix A, what is the corresponding eigenvalue?

Homework Equations




The Attempt at a Solution



4−λ 4 2
a b−λ c
d e f−λ=

det (λI3-3) =

−λ3+b+f+4×λ2+4×a−4×b+2×d+c×e−b×f−4×f×λ+−2×b×d+4×c×d+2×a×e−4×c×e−4×a×f+4×b×f

Don't know if I'm on the right track. Trying to find the roots of this characteristic equation, but there's so many unknowns.
 

Answers and Replies

  • #3
22
0
What is a eigenvector?
An eigenvector of A is a non-zero vector x such that Ax = λx
 
  • #6
22
0
Yes

24 a2-b+c10 d2-e+f10

I have 5 minutes left to answer the question. Would you mind helping me with the answer, and then you can explain it to me?
 
  • #7
13,827
10,995
Yes

24 a2-b+c10 d2-e+f10
I assume, this should be a column vector. Now what says the equation ##Ax = \lambda x## in the first coordinate?
 
  • #8
22
0
I assume, this should be a column vector. Now what says the equation ##Ax = \lambda x## in the first coordinate?
Sorry? You mean 24?
 
  • #9
22
0
I got it! Thanks!
 
  • #10
13,827
10,995
I mean the first coordinate is 24 on the left and ##\lambda x_1## on the right, yes.
 
  • #11
22
0
I mean the first coordinate is 24 on the left and ##\lambda x_1## on the right, yes.
I figured it out, thanks a bunch!
 

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