Decide whether or not the following functions are linear transformations. In each case give detailed and accurate reasons for your answer. Sketchy, poorly explained answers will not receive good marks! (a) 71 : 3 - R2 where Ti (x) = x . a x . b Here a and b are fixed vectors in R and the dot represents the dot product of two vectors. O T1 is a linear transformation. O T1 is not a linear transformation. Give reasons for your answer in the essay box. You may use any properties of dot products which you learned in MATH1131. : Q ZEquation A - A- BI US X2 X2 Styles Font Size we can prove this by the following conditions: 1. T(utv) = T(u) + T(v) 2. T(ku) = KT(U) Words: 18 (b) T2 : R2 -> R where T2 O T2 is a linear transformation. O T2 is not a linear transformation. Give reasons for your answer in the essay box. Q ZEquation A - A - IX BIUS X X Styles Font Size Words: 0 (c) T3 : P3 (R) - P3 (R) where T3 (p(x)) = p(x) - 5x2 +4x. O T3 is a linear transformation. O T3 is not a linear transformation. Give reasons for your answer in the essay box. = Q > Equation A . A- IX BIUS X2 XZ Styles Font Size