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Linear algebra, EE gate 2016
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Jun 29, 2017
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Linear Algebra
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rahul sharma 5
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eigen values will be 2,14... dont know about eigen vector..
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Answer is A. 2, 14,x1,x2
Correct me if I am Wrong
answered
Jun 30, 2017
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Arnab Bhadra
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So eigen vector of A^m is same as A and eigen vector of polynomial matrix equation given above will be same as A also?
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Yes... you can try for some examples the eigenvector for A turns out to be the same for A^m as well as the equation.
+1
@ Rahul
Yes they are same, see this
$ Ax = \lambda x \\ A^{^{2}}x = AAx = A\lambda x = \lambda Ax= \lambda \lambda x $
$A^{^{2}}x = \lambda^{2}x$
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Mathematics: GATE 2016 EE SET 1
Let the eigenvalues of 2 x 2 matrix A be 1, 2 with eigenvectors x1 and x2 respectively. Then the eigenvalues and eigenvectors of the matrix A^2  3A+4I would respectively, be (a) 2,14; x1,x2 (b) 2,14; x1+x2:x1x2 (c) 2,0; x1, x2 (d) 2,0; x1+x2,x1x2
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[Gate IN 2016 Set A] Linear algebra,Eigen values
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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