Simple eigenvector question - please evaluate

[enc08]

Hi,

$$A - I =\begin{bmatrix} -0.5253 & 0.8593 & -0.1906 \\ -0.8612 & -0.5018 & 0.1010 \\ 0.1817 & 0.1161 & -0.0236\end{bmatrix}$$

My eigenvector answer is

t= k(−0.0137,0.225,1)

My solution sheet's answer is

t = k(-0.0088, 0.216, 1)

Could I please ask that somebody checks this by hand? (not using an online solver as that's part of the problem).

A slightly awkward request but I appreciate anyone's answer.

I'm just seeking numerical confirmation. Thanks :)

(To save cluttering up this thread, I have already verified that I'm using the correct method here: https://www.physicsforums.com/showthread.php?t=668624)

 

[Mark44]

Hi,

$$A - I =\begin{bmatrix} -0.5253 & 0.8593 & -0.1906 \\ -0.8612 & -0.5018 & 0.1010 \\ 0.1817 & 0.1161 & -0.0236\end{bmatrix}$$

My eigenvector answer is

t= k(−0.0137,0.225,1)

My solution sheet's answer is

t = k(-0.0088, 0.216, 1)

Could I please ask that somebody checks this by hand? (not using an online solver as that's part of the problem).

A slightly awkward request but I appreciate anyone's answer.

I'm just seeking numerical confirmation. Thanks :)

(To save cluttering up this thread, I have already verified that I'm using the correct method here: https://www.physicsforums.com/showthread.php?t=668624)

I really don't want to go through all the arithmetic to hand-check your work, but you can check both purported vectors to see if either (or neither) works.

Let's call your vector x_enc08 = <−0.0137, 0.225, 1>, and the one from the solution sheet x_answer = <-0.0088, 0.216, 1>

Calculate (A - I)x for both vectors. If one of the vectors is an eigenvector (or close to it), the result should be close to <0, 0, 0>.

Since both vectors have a component of 1, it can't be the case that your vector is a scalar multiple of the one shown in the answer sheet.

 

[micromass]

Could I please ask that somebody checks this by hand?

Since it is your problem, wouldn't it make more sense that you check it by hand??