GATE 2012 ME HOW TO NORMAIZE EIGEN VECTORS

Question

Answer 1

 

Here eigen vector is (-1,1) and (3,1)

In option B) if we take common -1/√2 we get eigen vector (-1,1)

Comments

Not clear . Could you explain a bit

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ok?

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@srestha i know how to find eigen vector , I am confused with Normalised eigen vector and How did you get $\frac{-1}{\sqrt{2}}$

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I was missing this point https://gateoverflow.in/34573/gate-2012-what-is-normalised-eigen-vector
Thanks :)

Answer 2

Ans: B

step1: find out the eigen values - 6,2

step2: find eigen vectors for each

1) if you take 6 then 1 & 3 will come

2) if you take 2 then 1 and -1 will come (both are true as (1,-1) or (-1,1) )

step3: find out the component of the vectors.

for 6: sqare root((1-square) + (3-square) )  = sqrt(10)

for 2: sqare root((1square) + (-1square) )  = sqrt(2)

step4: divide vectors with its corresponding component.

(1/sqrt(2) , -1/sqrt(2) )  (or) (1/sqrt(10) , 3/sqrt(10) )

both are correct. we have first form is there at option B.

Comments

Thanks