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Unformatted text preview: Math 205, Spring 2006 B. Dodson New text - Peterson-Sochacki - 1. Course Info 2. Week 1 Homework: 1.1 (1st half), 1.2 Intro Due Thurs! - An m n matrix A is an array with m horizontal rows; n vertical columns i, j th entry a i,j in the i th row, and j th column. row vector or row n-vector, a, is a 1 n matrix, just one row. column vector or column n-vector, b, is a n 1 matrix, just one column. - Example. Give the rows and columns of A = 2 10 6 5- 1 3 . What are the entries a 1 , 2 , a 2 , 1 , a 3 , 1 , a 1 , 3 ? The matrix sum, A + B, is defined only when A and B have the same shape; and then the i, j th entry of A + B is a i,j + b i,j , the sum of the i, j th entries of A and B. 2 The scalar multiple of the matrix A by the scalar (number!) c is the matrix with the same shape as A, but with i, j th entry of ca i,j . Matrix multiplication: 1. row n-vector by column m-vector, only when n = m, is the number a 1 b 1 + a 2 b 2 + + a n b n , where the a i are the entries of a and the b i are the entries of b. 2. m n matrix A by p-column vector b, only when n = p, is the m-column vector with i th entry ( i th row of A ) b. Problem 3.2.11 Multiply A = - 1 2 4 7 5- 4 by c = 5- 1 . Solution: Ac = - 1 2 4 7 5- 4 5- 1 = (- 1)(5) + 2(- 1) 4(5) + 7(- 1) 5(5) + (- 4)(- 1) = - 7 13 29 ....
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