Mathematics II - Old Questions

18. What do you mean by basis change? Consider two bases B = {b₁, b₂} and c = {c₁, c₂} for a vector space V, such that  and Suppose  i.e., x = 3b₁ + b₂. Find [x]_c.

OR

Define basis of a subspace of a vector space.Let  where   and let  Show that span {v₁, v₂, v₃} = span {v₁, v₂}  and find a basis for the subspace H.