Please help me find the answers to the practice question and please provide work,

Exercise 7.5.2: Evaluating compositions. Let Ti : R3 - R3, T2 : R' _ R3, and T3 : R -> R' be linear transformations defined as follows. 1+2 T1 2+3 T2 = 21 - $2 T3 2 C1 - 22 C3 Find each composition, if the composition exists. (a (T2 0 71) 0 (b) (T2 0 T3) () (C) (Ti O T2) ( 3])Exercise 7.5.3: Matrix representation of a composition. Let 71 : R' -> R4 and 72 : R4 - R be linear transformations defined as follows. 2x1 1 2 T1 C1 = C1 - $2 1 + 2 = T2 3x2 E3 + 4 La1 + 5x2 Find the matrix representation for the composition given. (a) T2 o T1 (b) TioT2Exercise 7.5.4: Inverse linear transformations. Determine if each transformation is invertible. If so, give the matrix representation for the inverse transformation. (a) T : R' -> R given by T x1+ 2x2 232 (b) 2x2 - 3x3 T : R3 - R given by T = 4x2 + 6x3 T3 1 + 3x2 - 203Exercise 7.5.5: Finding the inverse of a composition of linear functions. Let 71 : R' -> R' and 72 : R' -> R be the invertible linear transformations defined as follows. T1 ([ = ]) 21 + 3x2 T2 2x1 + 5x2 -3x1 - 5x2 OC 2 3x1 + 702 Find the matrix representation for the inverse composition transformation given. (a (T2 o Ti) -1 (b) (TioT2)-1Exercise 7.6.2: Finding the matrix representation of a linear transformation with respect to nonstandard bases. Find [T']g for each of the given linear transformations and bases B and C. (a) T : R3 - R' defined by T 1 + 202 -203 O B = (b) T : P3 - R defined by a1 + 3a3 T (a1x3 + a2x2 + agx + a4) = a2 -5a4 B = {1, x, x + 2, 1+23); C= (c) T : P1 + P2 defined by T(aix + ao) = (a1 + 2ao)x2 - (a1 + ao)x + 300 B = {1, 1-x} , C = {1, x + 2,x2 - 1}