ME GATE 2012 What is Normalised Eigen Vector ?

Question

For the Matrix $\begin{bmatrix} 5 & 3\\ 1& 3 \end{bmatrix}$

One of the Normalised Eigen Vector is given as__________

Answer

  $\begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{-1}{\sqrt{2}}  \end{bmatrix}$

What is Normalised Eigen Vector ?
How to Find the Solution ?

Comments

I guess the answer must be:

$\begin{bmatrix} \frac{-1}{\sqrt{2}}\\ \frac{1}{\sqrt{2}}\\ \end{bmatrix}$

 

as given by @set2018.

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Original Question ^

Answer 1

Normalised eigen value is similar to unit vector.  i.e. if $[x_1,x_2] =  [a,b]$ is eigen vector then its normalized eigen vector will be

$=[a\div\sqrt{a_2+b_2}, b \div \sqrt{a_2+b_2}]$

 = [ a/√(a2+b2),b/√(a2+b2)]
Hence find the eigen vector first and divide it with its magnitude like above to get normalized eigen vector.

Comments

As per description given above, normalized eigen vector should be [  1/√2, 1/√2].(it will be column vector)

 

From where negative sign is coming???

Answer 2

https://math.stackexchange.com/questions/386623/finding-normalised-eigenvectors

https://core.ac.uk/download/pdf/9580718.pdf

Comments

can u upload a good quality image ?? hard to understand ...