Consider the ordered bases B = (1-8x, 9x- 1) and C = (x - 2,3+3x) for the vector space P2 r]. a. Find the transition matrix from C to the standard ordered basis E = (1, x). %3D Pec = b. Find the transition matrix from B to E. PE-B = c. Find the transition matrix from E to B. PB-E d. Find the transition matrix from C to B. PB-C e. Find the coordinates of p(x) = x - 3 in the ordered basis B. p(z)]B f. Find the coordinates of q(x) in the ordered basis B if the coordinate vector of q(x) in C is q(z)]c = (1, –1).

Consider the ordered bases B = = ((1,4), (2, 9)) and C = ((-1, 2), (3, -3)) for the vector space R². a. Find the transition matrix from C to the standard ordered basis E = ((1,0), (0, 1)). TE = b. Find the transition matrix from B to E. TE = c. Find the transition matrix from E to B. BE = ← A B ▶ ID ▲ ← - I- ▶ FI

2 Consider the matrix A = and the vector u = Let B = (A – A")2 and define vector v = Bu. If v = , write 1 down the value of vị. [Please enter your answer numerically in decimal format.

Help neeee in part a and B thanks in advance

Find the change-of-coordinates matrix from B to the standard basis in R". 8 3 3 B= 7 -3 - 4 8 P8 =

Consider the ordered bases B = ((-5, 3), (-2, 1)) and C = ((2, 1), (-3,4)) for the vector space R². a. Find the transition matrix from C to the standard ordered basis E = ((1,0), (0, 1)). TE b. Find the transition matrix from B to E. TE c. Find the transition matrix from E to B. d. Find the transition matrix from C to B. TB == 10 e. Find the coordinates of u [U]B=TB[U]E. [u]B == (-2, 2) in the ordered basis B. Note that f. Find the coordinates of v in the ordered basis B if the coordinate vector of vin C is [v] c = (1,2). [V]B=