In P2, find the change-of-coordinates matrix from the basis B = {1-3t+1²,2-5t + 31²,3 - 6t+7t²} to the standard basis C = {1,tt²}. Then find the B-coordinate vector for - 3+7t-4t².

Solve for C1, C3, C4, C5, & C6 without using matrix. Show the solution. C1-C3=1035.180 11C5+C6=-27829.395 6C1-6C3+C4=3346.704 C3-C5=2025 9C3+C4-9C5-C6=12149.514

Find the change of coordinates matrix, P, from C to B if B = {b₁,b₂), C = {c₁, c₂), b₁ = (7,-2), b₂ = (2, -1), c₁ = (4,1), c2 = (5,2) O P = [a₁ a₂], a₁ = (3,-2), a₂ = (8,-5) O P = [a₁ a₂], a₁ = (8,-5), a2 = (3,-2) ○ P = [a₁ a₂], a₁ = (2,-5), a₂ = (3,-8) OP [a1 a2], a₁ = = (3,-8), a2 = (2,-5) O P = [a₁ a₂], a₁ = (-3,2), a₂ = (-8, 5)

Calculate AB by two methods, first performing 2 matrix-vector multiplications and second by row- column multiplications A = -1 5 2 2 4 -3 B = 3 -2 -2 1