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Unformatted text preview: Chapter 2.4: Matrices Definitions and Some Operations Matrices can be represent other things than systems of equa- tions. Often, we use matrices to organize data. Example: An entrepreneur owns two jewelery stores, and takes inventory of sales of both stores. At the end of December, Store A had 42 bracelets, 93 necklaces, and 32 rings were sold. At the end of December, Store B had 12 bracelets, 82 necklaces, and 86 rings in were sold. The following matrix shows this data: bracketleftbigg 42 93 32 12 82 86 bracketrightbigg The first row represents the sales of Store A, and the second row represents the sales of Store B. The first column represents bracelets, the second column rep- resents necklaces, and the third column represents rings. We often name a matrix, using a capital letter. For this last example, we will say that A = bracketleftbigg 42 93 32 12 82 86 bracketrightbigg The numbers inside this matrix are called entries . The size of a matrix is expressed as (number of rows) (number of columns). In this last example, A has two rows, and three columns. We say that A is a 2 3 matrix. We can refer to a particular entry of A in the following way: a ij is the entry in matrix A which is in row i , column j . For example, a 12 = 93, as 93 is the entry which is in the 1 st row, 2 nd column of A . If a matrix consists of only one row, it is called a row matrix If a matrix consists of only one column, it is called a column matrix 1 If a matrix has the same number of rows as columns, it is called a square matrix Examples: B = bracketleftbig 0 9 8 12 bracketrightbig is a row matrix. C = 2 7 12 is a column matrix. D = - 15 7 4- 2 4 111 2 3- 14 10 2 is a square matrix. There are several operations which we can perform with matri- ces. Two operations are addition and subtraction. If two matrices are the same size, then we can add them to- gether. We do this by adding the corresponding entries....
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