Let α, β be two non-zero real numbers and v 1 , v 2 be two non-zero real vectors of size 3 × 1. Suppose that v 1 and v 2 satisfy v_{1}^{T}v_{2} = 0,v_{1}^{T}v_{1} = 1, and v_{2}^{T}v_{2} = 1. Let A be the 3 × 3 matrix given by: A = \alpha v_{1}v_{1}^{T} + \beta v_{2}v_{2}^{T} The eigenvalues of A are _______

0, \frac{\alpha + \beta }{2},\sqrt{\alpha \beta }

0, 0, \sqrt{\alpha ^{2} + \beta ^{2}}

GATE Electronics and Communications (EC) 2022 Solved Paper

Question : 43 of 65

Marks: +1, -0

Let α, β be two non-zero real numbers and v₁, v₂ be two non-zero real vectors of size 3 × 1. Suppose that v₁ and v₂ satisfy

v_{1}^{T}v_{2} = 0,v_{1}^{T}v_{1} = 1

, and

v_{2}^{T}v_{2} = 1

. Let A be the 3 × 3 matrix given by:

A = α v_{1}v_{1}^{T} + β v_{2}v_{2}^{T}

The eigenvalues of A are _______

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