Math 220 Spring 2023 Written Homework 5 Be sure to show all your work including each step of elimination and clearly indicate your nal answer. 1. A linear transformation T : 1R2 ) R2 rst reects points through the maxis and then reects points through the yaxis. (a) Find the standard matrix of T. (b) Show that T can also be described as a linear transformation that rotates points about the origin. What is the angle of this rotation? 2. The formula for a linear transformation T is given below. Determine if T is one-to-one, onto, both one-toone and onto, or neither. Marta] a: _ x + 2y 2 (MT 3; _[x+y+z] z :c x + y (c)T()= :c+2y I) 3y 1 2 1 2 1 . 3. Let A [_2 5 ] and B [ 6 _9 3 ]. Perform each computation below or explain why the operation is undened. (a) AB (e) A2 (b) BA . (c) ATB (0 Ad (6') BT24 (g) 32 4. Write each system in the matrix equation Ax = b. Find A1 if it exists and use it to solve for x. Otherwise, use Gauss-Jordan elimination. | :3 II o 2$+3y 4 2:1: + By (a) 43: 4y 12 03) 4:1: 4y $7y+22 (C) 3z+yz | N) H ,_. \f