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Unformatted text preview: of A be the rst column of the new matrix, and so on, we get a q p matrix A T , called the transpose of A . Transposes preserve scalar multiplication, addition, and subtraction, but reverse multiplication [Theorem 3, page 115]. What does this mean, exactly???? EXAMPLE. Suppose that A = " 1-2 1 3-4 5 # and B = 1 9-2 3 1 . Compute the following. 1. 2 A + 3 B T 2. AB 3. BA 4. B T A T . HOMEWORK: SECTION 2.1 EXAMPLES, IF TIME. Suppose the third column of matrix B is the sum of the rst two columns of B . What can you say about the third column of AB ? Why? Suppose A and C are matrices such that 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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