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Unformatted text preview: Math 330 Chapter 3 Quizzes Section 3.1  Take home assigned February 18, 2009 Suppose that A and the product AB are as given below. Determine B A = bracketleftBigg 1 1 3 bracketrightBigg AB = bracketleftBigg 2 2 0 0 6 0 1 bracketrightBigg SOLUTION: Since A is 2 2 and AB is 2 4 it must mean that B is 2 4. The 4 columns of AB come from come from linear combinations of the columns of A . Each column of B gives weights to produce the resulting column of AB . Let vectora 1 and vectora 2 denote the first and second columns respectively of A . Then we note the following about the columns vector c 1 ,vector c 2 ,vector c 3 , and vector c 4 of AB : By inspection vector c 1 = 2 vectora 1 + 0 vectora 2 . By inspection vector c 2 = 0 vectora 1 + 2 vectora 2 By inspection vector 0 = vector c 3 = 0 vectora 1 + 0 vectora 2 We can find the last column vectorx of B by solving the system Avectorx = vector c 4 : bracketleftBigg 1 1 3 bracketrightBigg bracketleftBigg b 14 b 24 bracketrightBigg...
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This note was uploaded on 09/19/2009 for the course MATH 330 taught by Professor Johnson,j during the Spring '08 term at Nevada.
 Spring '08
 Johnson,J
 Math, Linear Algebra, Algebra

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