Mathematics II - Old Questions

13. Define subspace of a vector space V. Given v₁ and v₂ in a vector space V, let H = span {v₁, v₂}. Show that H is a subspace of V.

OR

If  is a basis for a vector space V and x is in V, define the coordinate of x relative to the basis  . Let Then is a basis for H = Span {v₁, v₂}. Determine is X is in H, and if it is, find the coordinate vector of x relative to