Consider the bases B = {P₁, P₂} and B' = {₁,₂} for P₁, where P₁ = 6 + 3x, P₂ = 10 + 2x, q₁ = 2, q₂ = 3 + 2x a. Find the transition matrix from B' to B. b. Find the transition matrix from B to B'. c. Compute the coordinate vector [p]B, where p = −4+ x, and use (11) to compute [p]B¹. d. Check your work by computing [p], directly. 8. Let S be the standard basis for R², and let B = {V₁, V₂} be the basis in which v₁ = (2, 1) and v₂ = (−3, 4). a. Find the transition matrix PB-s by inspection. b. Use Formula (14) to find the transition matrix PS-B- c. Confirm that PB→s and Ps→B are inverses of one another. d. Let w = (5,-3). Find [w] and then use Formula (12) to compute [w]s. e. Let w = (3,-5). Find [w]s and then use Formula (11) to compute [w]B.