M313Lec03

M313Lec03 - Math 313 Lecture #3 1.3: Matrix Arithmetic,...

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Math 313 Lecture #3 § 1.3: Matrix Arithmetic, Part I Matrices and Vectors. An m × n matrix A = ( a ij ) is a rectangular array of mn numbers arranged in m rows and n columns: A = a 11 a 12 . . . a n 1 a 21 a 22 . . . a n 2 . . . . . . . . . . . . a m 1 a m 2 . . . a mn . The ( i, j ) entry of A is a ij ; it is the entry in the i th row and the j th column. Each row or column of a matrix is another matrix. A 1 × n matrix (one row) is called a row vector , and an n × 1 matrix (one column) is called a column vector . [Each of these is an n -tuple of real numbers.] The collection of all n × 1 matrices is called Euclidean n-space and is denoted by R n . A solution of a consistent m × n system will be represented by column vector, or simply a vector in R n : ~x = x 1 x 2 . . . x n . [The textbook uses the bold notation x for a vector, but this is not feasible when writing on the chalkboard. Remember that ~x x .] The i th row of an m × n matrix A = ( a ij ) is denoted by ~a ( i, :) = ( a i 1 , a i 2 , . . . , a in ) , i = 1 , . . . , m The j th column of an m × n matrix A = ( a ij ) is denoted by ~a (: , j ) ~a j = a 1 j a 2 j . . . a
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M313Lec03 - Math 313 Lecture #3 1.3: Matrix Arithmetic,...

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