Let {f1, f2, f3} be the dual basis of {e1, €2, €3} for R³, where e₁ = (1, 1, 1), €₂=(1,1,−1), Find f₁(x), f₂(x), f3(x), where x = (1, 0, 0). €3=(1,−1,−1).

Given basis B = {(1, -1), (2, 3)} and basis C = {(1, 0), (0, 1)}, and linear map T = (x + 2y ; 2x - y) from R2 --> R2, find the coordinate vectors of basis C in terms of basis B.

3. Do the vectors (1, 1,0), (0, 1, 1) and (1,0, –1) form a basis of R3?

The vectors p1(t) = 1 + t², p2(t) = −t + 3t², and p3(t) = 1+t+t2 form a basis B 2(t), p3(t)} for P₂(R). Let p(t) = 1 + 2t + 4t², find its B-coordinates [p(t)B. =