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Unformatted text preview: , called the transpose of A . Transposes preserve scalar multiplication and addition/subtraction, but reverse multiplication [Theorem 3, page 115]. EXAMPLE. Suppose that A = " 12 1 34 5 # and B = 1 92 3 1 . Compute 2 A +3 B T , AB , BA , and B T A T . HOMEWORK: SECTION 2.1 EXAMPLES, IF TIME. Suppose the third column of B is the sum of the rst two columns of B . What can you say about the third column of AB ? Why? Suppose CA = I n . Show that the equation A x = has only the trivial solution. Explain why A cannot have more columns than rows....
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This note was uploaded on 04/15/2008 for the course M 340L taught by Professor Pavlovic during the Spring '08 term at University of Texas at Austin.
 Spring '08
 PAVLOVIC
 Linear Algebra, Algebra, Matrices, Scalar

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