1. Explain why, for an arbitrary vector x ∈ Rn and an arbitrary scalar a ∈ R, kaxk = akxk. 2. For any two vectors x, y ∈ Rn, we have kxk + kyk ≥ kx + yk. Under precisely what circumstances do we have...

1. Explain why, for an arbitrary vector x ∈ Rn

and an arbitrary scalar a ∈ R, kaxk = akxk.

2. For any two vectors x, y ∈ Rn, we have kxk + kyk ≥ kx + yk. Under precisely what circumstances do we have kxk +kyk = kx + yk for x, y ∈ Rn? Explain briefly