GATE Computer Science (CS) 2018 Shift 1 Solved Paper

Question : 32 of 65

Marks: +1, -0

Consider a matrix

A=u v^{T}

where

u=(\table 1 ; 2), v=(\table 1 ; 1) .

Note that

v^{T}

denotes the transpose of

v

. The largest eigenvalue of

{A}

is ──────.

Solution:

u=(\table 1 ; 2), v=(\table 1 ; 1)

A=u V^{T}

=[\table 1 ; 2][\table 1 , 1]

=[\table 1 , 1 ; 2 , 2]

(1-λ)(2-λ)-2=0

λ^{2}-3 λ=0

λ(λ-3)=0

λ=0

or,

λ=3

The largest eigen value is

3 .

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