Let A be the 2 x 2 matrix with elements a11 a12 a21 1 and a22 1 Then the eigen values of the matrix A19 are gate computer science 2012
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Let A be the 2 x 2 matrix with elements a11 = a12 = a21= + 1 and a22 =-1. Then the eigen values of the matrix A19 are -gate-computer science-2012

Let A be the 2 x 2 matrix with elements a11 = a12 = a21= + 1 and a22 =-1. Then the eigen values
of the matrix A19 are
 (A) 1024 and -1024 (B) 1024 2 and 1024 2
 (C) 4 2 and 4 2 − (D) 512 2 and 512 2


By:Amogh

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Answers

Answer: (D) 
Explanation:
A =  1    1
     1   -1

A2 = 2   0
        0   2

A4 = A2 X A2
A4 = 4   0
         0   4

A8 = 16   0
        0    16


A16 = 256   0
           0    256

A18 = A16 X A2
A18 = 512   0
           0    512 

A19 = 512   512
          512  -512


Applying Characteristic polynomial

512-lamda   512
512       -(512+lamda)  =   0

-(512-lamda)(512+lamda) - 512 x 512 = 0

lamda2 = 2 x 5122 


milan-ransingh

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