Math 11044/Linear Algebra Assignment #2 * Answer the questions below, showing all relevant work and the methods used to obtain your results. Answers may only be submitted as a single PDF (.pdf) file. . Submit your answers on SLATE by the due date specified on SLATE. . This is an individual assignment. Assignments copied in whole or in part will receive a grade of ZERO. Questions: 1. H = { (x, y,z)|2x - y + 32 = 0]. Is H a subspace? Justify your answer. (2 marks) 2. Let Y = span(2 - x + x2,3+ 4x -x?, 1+ 27x -12x?). Find a basis for Y and state the dimension of Y. (2 marks) 3. Let u = (-4,3,8) and v = (1, -2,6). (2 x 2 marks) a. Find a vector w such that the parallelepiped P generated by {u, v, w) has a volume of 48 units b. Suppose the volume of T(P) is 22 units and 7: IR3 - R3 is a linear transformation. Find the possible value(s) of det A if A is the matrix of T. 4. Let Qo : IRZ - RZ be reflection in the x axis, let Q1 : IRZ - R be reflection in the line y = x, and let RT/2: RZ - RZ be counterclockwise rotation through n/2. (2 x 1 mark) a) Show that Q1" Rx/2 = 20 b) Show that Ru/2 " 20 = Q1