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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 âˆ’ (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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