assignment3 - a) 1 , 1 1 1 , 1 1 , 1 1 ; b) {1 + x, x + x 2...

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University of Toronto at Scarborough Department of Computer and Mathematical Sciences Linear Algebra II MATB24 Fall 2010 Assignment # 3 You are expected to work on this assignment prior to your tutorial in the week of October 4th, 2010. You may ask questions about this assignment in that tutorial. In your tutorial in the week of October 11th you will be asked to write a quiz based on this assignment and/or related material from the lectures and tutorials in week 3 and textbook readings. Textbook: Linear Algebra by Fraleigh & Beauregard, 3rd edition. Read: Chapter 3 Section 2 and week 3 Lecture Notes Problems: 1. , Pages 202-203 # 12, 13, 16, 17, 19, 20, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37. 2. Addition: 1) Determine whether the following sets are linearly independent.
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Unformatted text preview: a) 1 , 1 1 1 , 1 1 , 1 1 ; b) {1 + x, x + x 2 , x 2 + x 3 , x 3 }. 2) Exhibit a basis of each of the following subspaces of the spaces indicated. a) {p(x) | p(x)= p( x)}; in P 2 . b) 1 1 A A ; in M 22 . 3) Let A 0 and B 0 be n n matrices, and assume tat A is symmetric and B is skew-symmetric (that is, B T = B ). Show that the set {A, B} is independent. Note: There are answers at the back of the textbook for the odd number questions....
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