mws_gen_sle_bck_introduction - Chapter 04.01 Introduction...

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04.01.1 Chapter 04.01 Introduction After reading this chapter, you should be able to 1. define what a matrix is . 2. identify special types of matrices, and 3. identify when two matrices are equal. What does a matrix look like? Matrices are everywhere. If you have used a spreadsheet such as Excel or Lotus or written a table, you have used a matrix. Matrices make presentation of numbers clearer and make calculations easier to program. Look at the matrix below about the sale of tires in a Blowoutr’us store – given by quarter and make of tires. Q1 Q2 Q3 Q4 Copper Michigan Tirestone 6 5 25 16 10 20 7 15 3 27 25 2 If one wants to know how many Copper tires were sold in Quarter 4 , we go along the row Copper and column Q4 and find that it is 27. So what is a matrix? A matrix is a rectangular array of elements. The elements can be symbolic expressions or numbers. Matrix ] [ A is denoted by mn m m n n a a a a a a a a a A ....... ....... ....... ] [ 2 1 2 22 21 1 12 11 Row i of ] [ A has n elements and is
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04.01.2 Chapter 04.01  in i i a a a .... 2 1 and column j of ] [ A has m elements and is mj j j a a a 2 1 Each matrix has rows and columns and this defines the size of the matrix. If a matrix ] [ A has m rows and n columns, the size of the matrix is denoted by n m . The matrix ] [ A may also be denoted by n m A ] [ to show that ] [ A is a matrix with m rows and n columns. Each entry in the matrix is called the entry or element of the matrix and is denoted by ij a where i is the row number and j is the column number of the element. The matrix for the tire sales example could be denoted by the matrix [ A ] as 27 7 16 6 25 15 10 5 2 3 20 25 ] [ A . There are 3 rows and 4 columns, so the size of the matrix is 4 3 . In the above ] [ A matrix, 27 34 a . What are the special types of matrices? Vector: A vector is a matrix that has only one row or one column. There are two types of vectors – row vectors and column vectors.
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This note was uploaded on 06/12/2011 for the course EML 3041 taught by Professor Kaw,a during the Spring '08 term at University of South Florida.

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mws_gen_sle_bck_introduction - Chapter 04.01 Introduction...

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