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**Unformatted text preview: **Week 3 2.1 Matrix Algebra So far, we have used augmented matrices to abbreviate systems of linear equations. However, in general, a matrix can be any rectangular array of numbers, called entries . The size of a matrix is defined by the number of rows and columns it contains. An m n matrix has m rows ad n columns. ex. 1 2 3- 1 4 A matrix with n rows and only 1 column is called a column matrix or column vector . ex. a 1 a 2 . . . a n A matrix with 1 row and n columns is called a row matrix or row vector . b 1 b 2 b n A matrix with n rows and n columns is called a square matrix . We usually denote matrices by capital letters and the entries with subscripts depicting their position in the matrix. Definition: The ( i, j )- component of an m n matrix A is the entry in row i and column j of A and is denoted a ij or ( A ) ij . A = a 11 a 12 a 1 n a 21 a 22 a 2 n a 31 a 32 a 3 n . . . . . . . . . a m 1 a m 2 a mn Note: { a 11 , a 22 , . . . a mm is called the main diagonal of A . Special Matrices A diagonal matrix is a square matrix whose entries off the main diagonal are all 0. An identity matrix is a square diagonal matrix whose entries along the main diagonal are 1. 1 Operations with Matrices Equality Two m n matrices are equal if they have the same size and their corresponding entries are equal....

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