- #1

- 7

- 0

[0 0 a

0 0 0

0 0 0]

please elaborate ur answer!!

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- Thread starter flash123
- Start date

- #1

- 7

- 0

[0 0 a

0 0 0

0 0 0]

please elaborate ur answer!!

- #2

- 631

- 0

Have you checked out the rules? Pretty cool stuff there!

In particular, we cannot provide answers to your questions. We can (and will, to the best of our ability) help you find it. So, you have to show us some effort from your side.

If you know nothing about eigenvectors, Google is a good place to start.

- #3

- 7

- 0

i got eigen values as 0, 0 , 0

and after using [A-lambdaI]X=0

i am getting 0X1+0X2+aX3=0

which makes eigen vector as [0 0 0 ]

whereas the answer is [0 0 a]

- #4

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 963

- #5

- 7

- 0

but after solving the eqn [A-lamdaI][X]=0 or AX=lamdaX

i got az+0+0 = 0

so how to proceed further and arrive at the correct answer?

- #6

HallsofIvy

Science Advisor

Homework Helper

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What do you mean "the answer is ..."? Do you understand **what** an eigenvector is? If a given vector is an eigenvector so is any multiple of it. You **cannot** just say "the eigenvector" is any specific vector. I said before, "we must have z= 0. We have NO information about x or y so they can be anything."

That includes your [a, 0, 0], taking x= a, y= 0. It also includes [1, 0, 0], [0, 0 1], and any linear combination x[1, 0, 0]+ y[0, 1, 0]= [x, y, 0].

For**any** x, y,

[tex]\begin{bmatrix}0 & 0 & a \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}\begin{bmatrix}x \\ y \\ 0\end{bmatrix}= \begin{bmatrix}0 \\ 0 \\ 0\end{bmatrix}= 0\begin{bmatrix}x \\ y\\ 0\end{bmatrix}[/tex]

That includes your [a, 0, 0], taking x= a, y= 0. It also includes [1, 0, 0], [0, 0 1], and any linear combination x[1, 0, 0]+ y[0, 1, 0]= [x, y, 0].

For

[tex]\begin{bmatrix}0 & 0 & a \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}\begin{bmatrix}x \\ y \\ 0\end{bmatrix}= \begin{bmatrix}0 \\ 0 \\ 0\end{bmatrix}= 0\begin{bmatrix}x \\ y\\ 0\end{bmatrix}[/tex]

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- #7

- 7

- 0

since x and y could be anything

so the possible eigen vectors corresponding to eigen value 0 are

[1 0 0],[0 1 0] or [1 1 0]

please tell me am i correct now?

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