engineering recuitment GATE ECE 2023-24 Test Series Engineering Mathematics Linear Algebra Eigenvalues
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 \(v_1^Tv_2=0, v_1^Tv_1=1\), and \(v_2^Tv_2=1\). Let A be the 3 × 3 matrix given by:
\(\rm A=\alpha v_1v_1^T+\beta v_2v_2^T\)
The eigenvalues of A are _______
1
0, α, β
2
0, α + β, α - β
3
0, \(\frac{\alpha+\beta}{2}, \sqrt{\alpha \beta}\)
4
0, 0, \(\sqrt{\alpha^2+\beta^2}\)