Assignment #7 - Stephanie Campbell due at 11:59pm EST...

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Stephanie Campbell Assignment 7 MATH133, Fall 2009 due 11/21/2010 at 11:59pm EST. You may attempt any problem an unlimited number of times. 1. (1 pt) Which of the following transformations are linear? A. y 1 = 9 x 1 + x 2 y 2 = - x 1 B. y 1 = x 2 2 y 2 = x 3 y 3 = x 1 C. y 1 = 0 y 2 = 7 x 2 D. y 1 = 8 x 2 y 2 = - 3 x 3 y 3 = - 6 x 1 E. y 1 = x 1 + 2 y 2 = x 2 F. y 1 = 9 y 2 = 7 y 3 = 8 2. (1 pt) Find the matrix M of the linear transformation T : R 2 R 2 given by T x 1 x 2 = - 5 x 1 + 7 x 2 8 x 1 + x 2 . M = . 3. (1 pt) If T : R 2 R 2 is a linear transformation such that T 1 0 = -4 5 and T 0 1 = 10 -9 , then the standard matrix of T is A = . 4. (1 pt) If T : R 3 R 3 is a linear transformation such that T 1 0 0 = 4 1 4 , T 0 1 0 = -4 -2 -1 , and T 0 0 1 = 4 2 2 , then T -1 -2 0 = . 5. (1 pt) Find the matrix M of the linear transformation T : R 3 R 2 given by T x 1 x 2 x 3 = 4 x 1 + x 2 + 8 x 3 - 2 x 1 + 5 x 3 .
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