7. Let B = {(1,2,3), (2,0, 4), (1, 1, 1)}. Prove that B is a basis for R³ (since this is a proof, you must give an explanation, simply doing some algebra by itself is not enough).

9. Determine whether the set of vectors i (2,-1), (3,-2), (0, 1)} is basis for TR? a

2) Determine whether S = {(0,3, -2), (4,0,3)(-8,15, -16)} is a basis for R3.

Show that B = {1,1 – x, 2 – 4x + x², 6 – 18x + 9x² – x³} is a basis for P3(R). Hint: Recall that dim(P3(R)) = 4 and note that B has 4 vectors.