Let {u1, u2} and {v1, v2} be ordered bases for R2, where (a) Determine the...

Let {u₁, u₂} and {v₁, v₂} be ordered bases for R², where

(a) Determine the transition matrix corresponding to a change of basis from the standard basis {e₁, e₂} to the ordered basis {u₁, u₂}. Use this transition matrix to find the coordinates of x = (1, 1)^T with respect to {u₁, u₂}.

(b) Determine the transition matrix corresponding to a change of basis from the basis {v₁, v₂} to the ordered basis {u₁, u₂}. Use this transition matrix to find the coordinates of z = 2v₁ +3v₂ with respect to {u₁, u₂}.