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If we solve this we will get total 4 eigen vectors,but as we know that this is of 2 degree matrix so only 2 will exist.So can i say that from these four pairs by using nay 2 ,i can derive the other?If yes,then how?

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answer will be (A)...and why you will get 4 eigen vectors, only 2 eigen vectors corresponding to 2 eigen values....if you are saying in this sense """""one time take x as arbitary next time take y as arbitary""""".....it will not make 4 eigen vector, it is still two eigen vectors, because ultimately you will take out common arbitary...

i dont know if you understand what i am saying..
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Answer is both a and c and it was marks to all
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how option 'c' could be answer??....in second pair of eigenvector [0 1], it is not possible because here x=0 and since either x or y is linearly dependent on other then other should also be 0...
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what will be its eigen values and vector please explain
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here , there will be two eigen vectors ({1,-j} corresponding to eigen value i  and {j,-1} corresponding value -i).

,Since the eigen value is j, and -j finding the corresponding eigen vector, which gives  {1 -i} and {i,-1} respectively

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