MATH
253Homework3

# Linear Algebra with Applications (3rd Edition)

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ma253 , Fall 2007 — Problem Set 3 This problem set deals mostly with linear transformations and matrices, but there’s also some stuff about more general linear spaces. As usual, solve all the problems, then write up and turn in those marked with an asterisk. This assignment is due on Wednesday, October 3 . 1. Problems from the textbook: a. Section 2 . 1 , problems 1 , 3 , * 4 , 5 , * 6 , 9 , * 10 , * 16 , 18 , 19 , * 20 , 24 30 . 40 , * 49 , * 52 . b. Section 2 . 2 , problems 1 , 4 , 5 , 7 , * 18 , 19 , * 34 c. Section 2 . 4 , problems 1 13 , * 14 , 15 , * 16 , 17 , 19 , * 20 , * 76 2. The matrix A = - 0.6 1 0 - 0.4 0 1 , corresponds to a linear transformation T : R 3 R 2 . Consider the unit cube in R 3 defined by the standard basis vectors e 1 = 1 0 0 e 2 = 0 1 0 e 3 = 0 0 1 . In R 2 , draw the image under T of each of these vectors and of the unit cube they determine. 3. The matrix A in the previous problem gives one way to represent three-dimensional objects on a two-dimensional page. Does A send any non-zero vectors in R 3 to the zero vector in R 2 ? In terms of the interpretation of the matrix as a way to “draw”

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