# 2-4 - Chapter 2.4 Matrices Definitions and Some Operations...

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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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## This note was uploaded on 02/05/2011 for the course MATH 377 taught by Professor Stephenlang during the Spring '11 term at University of Victoria.

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2-4 - Chapter 2.4 Matrices Definitions and Some Operations...

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