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(3) Let T : P3(R) = M2x2(R) Be The Linear Transformation Given By T(a + Br + C22 + 3 (a+b A – 2c (

(3) Let T : P3(R) = M2x2(R) be the linear transformation given by T(a + br + c22 + 3 (a+b a – 2c (a) Find the null space of T. [2] (b) Show that I is invertible without giving an explicit inverse. [2] (c) Find the matrix representation (T); for bases 1,0,19,2"}, = {(6 %) (0 o) ( ) ( )}. [2] (a) Compute ([T]%)-1 and use this to find an expression for 7-1, i.e. find (e) Consider the 2 x 2 identity Find its pre-image in P (Runder Two Ways (i) by computing T I) nsing the result fr?m (a) (1) (ii) by first finding [/2. then computing ([]-17 11