EC > GATE 2022 > Linear Algebra
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 v1T v2 = 0, v1T v1 = 1, and v2T v2 = 1. Let A be the 3 × 3 matrix given by:
A = αv1v1T + βv2v2T
The eigenvalues of A are __________.
A
0, α, β
B
0, α + β, α − β
C
0, (α + β)/2, √(αβ)
D
0, 0, √(α2 + β2)

Correct : a

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