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Module 4 Matrices

Overview of matrices: rectangular arrays of numbers, defining rows/columns and entries. Covers dimensions (m×n), locating entries, types (square, row, column matrices), and using matrices for computations (e.g., soccer equipment costs).

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Finite M a t hM o d u l e 4: MatricesReading: Matricesand Matrix OperationsTwo club soccer teams, the Wildcats and the M u d Cats, are hoping to obtain new equipment for an upcoming season.Table 1 shows the needs of both teams.Table 1W i l d c a t s M u d CatsGoals610Balls3024Jerseys1420A goal costs $300; a ball costs $10; and a jersey costs $30. How can we find the total cost for the equipment needed for each team? In thissection, we discover a method i n which the data i n the soccer equipment table can b e displayed and used for calculating other information.Then, we will b e able to calculate the cost o f the equipment.Finding the Sum and Difference of Two MatricesTo solve a problem like the one described for the soccer teams, we can use amatrix,which is a rectangular array of numbers. Ar o win a matrix isa set of numbers that are aligned horizontally. Acolumni n a matrix is a set o f numbers that are aligned vertically. Each number is anentry,sometimes called an element, of the matrix. Matrices (plural) are enclosed i n [ ] or ( ) , and are usually named with capital letters. For example,three matrices named and are shown below.A=\matrix{{1}&{2}\\{3}&{4}}\displaystyleB = \begin{bmatrix}{1}&{2}&{7}\\{0}&{5}&{6}\\{7}&{8}&{2}\end{bmatrix}\displaystyleC = \begin{bmatrix}{1}&{3}\\{0}&{2}\\{3} & {1}\end{bmatrix}Describing MatricesA matrix is often referred to by its size or dimensions:m x nindicatingmrows and n columns. Matrix entries are defined first by row and then by column. For example, to locate the entry i n matrix Aidentified asaywe look for the entry in rowj columnIn the matrix shown below, the entry in row 2, column 3 is a2 3 =a_lla_21a_31a_12a_22a_32a_13"a_23a_33

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