Let $$\alpha$$, $$\beta$$ two non-zero real numbers and v1, v2 be two non-zero real vectors of size 3 $$\times$$ 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 $$\times$$ 3 matrix given by :
A = $$\alpha$$v1$$v_1^T$$ + $$\beta$$v2$$v_2^T$$
The eigen values of A are __________.
- A0, $$\alpha$$, $$\beta$$
- B0, $$\alpha$$ + $$\beta$$, $$\alpha$$ $$-$$ $$\beta$$
- C0, $${{\alpha + \beta } \over 2},\sqrt {\alpha \beta } $$
- D0, 0, $$\sqrt {{\alpha ^2} + {\beta ^2}} $$
✓ Correct answer: A
Want the full step-by-step reasoning?