Please show work for

2. Now consider U : M2x2 (R) - P:2(R) defined by " ( (" 4) ) - ( a+ b ) + (20) + ca? T: P&2(B) - Max2 (B) defined by I(p(2):= (.(@) 2p(1) a) Find the compositions UT, TU, where T is the linear transformation defined in question 1. (Namely, write the rules of UT and TU.) b) Represent U. UT, TV by matrices using the bases B1, B2 given in question 1. (namely, find [UlB,, [UT]B,, [TU]B, after figuring out the suitable values for ?'s). c) Almost done. Compute [Ulg: [Tig, and [T] [U]g, after figuring out ?'s. And check your answer from part (b). You did multiply matrices in (c), but do you really know how to multiply matrices? d) Consider AB = C. Fill in the blanks using the words below (one word per blank space): ith, jth, A, B, all, column(s), row(s). If I'm in a hurry and need to compute cy, then I use of A and of B. To compute the it row of C, I use of A and of B. So the ith row of C is a linear combination of of with coefficients coming from of To compute the jth column of C, I use of A and of B. So the joh column of C is a linear combination of of with coefficients coming from of