MA1200 A2 F23 Assignment 7 Name: Total Marks: 20 Due Nov 7 1. Recall that Q_1:I1R2 > R2, reflection in the line y : a) [2 marks] Find MQ_1 and use this matrix to find Q_1(x) wherex : (2, 3). b) [4] Use matrices to express Q_1 as the composition of a rotation followed by reflection in the line y : x. 2. [6: 3 each] In each case, find the standard matrix for T: R2 R2 and thereby show that T either a reflection in a line, orthogonal projection onto a line, or rotation through an angle. Find the line (in the case of a reflection or projection) or angle (in the case of a rotation.) a) T( ([37]): 54112:); bl T (El) : ' 1 Jary] 4 2 2 x\" ,5. c) T(l)'l):5 21" +1] 3. [6: 3 each] In each case, use matrix multiplication to find a rotation or reflection that equals the given transformation. a) Reflection in the y axis followed by rotation through?. b) Reflection in the x-axis followed by reflection in the line y = x. (You'll also use the fact that Ms = My implies S = T.) 4. [2] Show that T: R2 - R2 defined by T(x, y) = (xy, 0) is not a linear mapping. To do this, either i) Find specific vectors x, y E R2 such that T(xty) # T(x) +T(y) or ii) Find a specific r E R and x E R2 such that T(rx) # rT(x)