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Unformatted text preview: Math 205, Spring 2010 Week 2 (continued): 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, vectora, is a 1 n matrix, just one row. column vector or column n-vector, vector b, is a n 1 matrix, just one column. 2 Example 1. Give the rows and columns of A = parenleftbigg 2 10 6 5- 1 3 parenrightbigg . 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. 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 vectora and the b i are the entries of vector b....
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- Spring '08