Please finish Example 1:

756 CHAPTER 11 Systems of Equations and Inequalities We can arrange these data in a rectangular array as follows: or as the matrix [200 150 45] 315 125 65 senting male and female) and th \"no opinion\"). Tee Colu \"In: I two rows (repre This matrix has \" \"too low,\" and (representing \"too high, oped in Examp d n columns is called a y 3 matrix and contains The matrix devei matrix with m rows an in Example 1 is a 2 b contains m - n entries. If an m by n matrix then the matrix is a square matrix. i EXAMPLE 2 Examples of Matrices 5 0 (a) [-6 1] A2by25quarcmalrix (b) [1 O 3] A1by3mm a 'x has the same number of rows as COIUmns, that ' IS, if m ' ' n 6 -2 4 (C) 4 3 5 A 3 by 3 square matrix 8 0 1 I 11' Find the Sum and Difference or Two Matrices We begin our discussion of matrix algebra b rst ' ' Illlleegiedleetgliigo the operations of addition and {subtra2:153:11.l III? izcilrltlilplzlrim matrices and number of 001 31511 rlequtre both matrlces to have the same number of rovin t to note that Matrices usualsl as a condition for equality and for addition and s and the same y are represented by capital letters, such as A summon\" D . EFl NITION Two matrices A and B are equal, written as provided that A and B h ave the same number of rows and the same number ['1' m n I For example, I: 2 1] V4: 1 0'5-1--l and[321_\\/\\ 1 '1 0 1 -2 _ o 1 \\3/:S [4 1 4 0 6 1 75 6 1] Bee ~ - - arise the entries 1n row 1, column 2 are not equal 4 [6 i 3] 9e [4 1 2 3 6 1 2 4 Because the matrix on the left has3columns and the matrix on the right has 4 columns SUPP'Ne 1| ' lat A a "d 3 represent two m by n matrices. The sum, A +B, is defined as iii A , - e m by n - and b0 "1 B. The diam?" fOrrned by adding the corresponding entries 0;; 0f cc, A ' B. is defined as the m by n matrix formed by subtractin g [he emf res - by 1n B from the corresponding entries a; in A. Addition and tam Your Knowledge sermon 11.4 Matrix Algebra 765 Re 70'73 are based on material learned eariie It ' prob a! on are better r r m lh , [\"0 th V P cpared for the lm! ex e Course. The purpose of these problems is to keep the material fresh in your mm ' ~ am. rthe Pomts P (-4,3) and = 10-11:,"+ bj and find \"v". Q (5,-1) List the potential rational zeros of the pol \"'Gmphx) = (x +1)2 :Find the exact value of t wt. \\ d n \"e the vector v represented by the directed line segment PQ 1n the form ynomial function P( _ ' x) = 2x3 _ 5x2 + 10- 4 using transformations (shifting x an 42 _ _ compressing, stretching. and/or reecting). cot 48 Without using a cal culalor. 11.4 Matrix Algebra OB ' JECTIVES 1 Flnd the Sum and Difference of Two Matrices (p. 766) 2 Find Scalar Multiples of a Matrix (p. 768) 3 Find the Product of Two Matrices (P- 759) 4 Find the inverse of a Matrix (p. 773) 5 Solve a System of Linear Equations Using an Inverse Matrix (9- 775) ' . TFVMrwv -\"WW . -wmwMM .wnmwwmv -- mm "a.\" m \"Mfrs. awn-e ' m. . We... Wm gumnur- : - ' "' ' ' Section 11.2 dened a matrix as a rectangular array of real numbers and used an augmented matrix to represent a system of linear equations. There is, however, a branch of mathematics, called linear algebra, that deals with matrices in such a way that an algebra of matrices is permitted. This section provides a survey of how thls matrix algebra is developed. Before getting started, recall the denition of a matrix. DEFINITION A matrix is a rectangular array of numbers: Column 1 Column 2 Column j Column 1: ROW 1 an an ' ' ' (11} 01,, ROW 2 (121 (122 (12} a2" ROW i 11,1 (1,2 all am Rowm am] am; - - - am]. . . . am" Each number up of the matrix has two indexes: the row index i and the column index j. The matrix shown here has m rows and n columns. The numbers ail- are the entries of the matrix. For example, an refers to the entry in the second row, third column. Arranging Data in a Matrix In a survey of 900 people, the following information was obtained: 200 males Thought federal defense spending was too high 150 males Thought federal defense spending was too low 45 males Had no opinion 315 females Thought federal defense spending was too high 125 females Thought federal defense spending was too low 65 females Had no opinion