Can someone help me with these questions?

The change of basis questions are pretty confusing.

1. (a) Find the transition matrix P\"; from the basis % to the standard basis 9:, where 83 = {(1, 2, 1), (0, 3, 2), (1, 0, 1)}, Q: :{(1,0,0), (0,1, 0), (0,0,1)}. (b) Compute Paar- (c) Use Pang to nd [(13% where :1: : (4,8,4). 2. (a) Write the standard basis representation for the map S : 1R3> R3 which dilates by a factor of 2 along the xaxis and reects over the cry plane. (Your answer should be a 3 x 3 diagonal matrix.) (b) Now consider the basis % = {(31, b2, (93} from question 1 (so 191 = (1, 2, 1) and so on) and the unique linear map T: R3 ) R3 with action T(b1) : 2b1, T(b2) : b2, T(b3) : b3. Find [T]3. Hint: don't work hard! (c) Now nd the standard basis representation [T] with Q: also as in question 1. (d) Is the matrix [T] invertible? Justify your