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(1) Let T : P3(R) ? M2x2(R) Be The Linear Transformation Given By T(a+bx+cr? + Dr3) – ( 3a + 76

(1) Let T : P3(R) ? M2x2(R) be the linear transformation given by T(a+bx+cr? + dr3) – ( 3a + 76 - 2c-5d 8a + 146 - 2c - 110 -40 - 86 + 2c + 6d 12a + 225 - 4c - 170) (a) Find the matrix representation T for bases B = {1,2,2", 1"},7 B = {1, 2, 22, 23), 7= (10.01) (0 0) (00) 1 o o o o 1 0 (b) Find the matrix representation (T% for bases B = {1+ 1 - + 273,-1+ 2x + 27% 2+1 – 222 + 38",1+1 +22}, c={(- 9) (2) (2, 3) 6 2)}. [2] (c) Let p(x) = 3 - 2 + 2x2 – 51°. Find (p(x)]s and (p(x)]B. (d) Find the image of p(2) under T in the following three ways: (i) by computing T (p(r)) directly, [1] (ii) by computing (T];[p(x)]= (T(p(2)],, [1] (iii) by computing (T]P(r)]B = [T(p()]c. [1] (e) Compute the matrix representations (1) and (0)8, where I is the identity map on P3(R). Show that (1) Compute the matrix product 1181 about the result? 8. What do we notice