View of /trunk/NationalProblemLibrary/ASU-topics/set119MatrixAlgebra/p33.pg

    1 ## DESCRIPTION
    2 ## Matrix Algebra
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Algebra' 'Matrix' 'Matrices' 'True' 'False')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Algebra')
    9 ## DBchapter('Systems of Equations and Inequalities')
   10 ## DBsection('The Algebra of Matrices')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('ASU')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PGasu.pl",
   24 "PG.pl",
   25 "PGbasicmacros.pl",
   26 "PGchoicemacros.pl",
   27 "PGanswermacros.pl",
   28 "PGauxiliaryFunctions.pl",
   29 "PGmatrixmacros.pl"
   30 );
   31 
   32 TEXT(beginproblem());
   33 $showPartialCorrectAnswers = 1;
   34 
   35 $microA1 = random(30,60);
   36 $fridgeA1 = random(10,30);
   37 $stoveA1 = random(20,50);
   38 $microA2 = random(25,55);
   39 $fridgeA2 = random(12,40);
   40 $stoveA2 = random(15,45);
   41 
   42 $microX1 = random(30,60);
   43 $fridgeX1 = random(10,30);
   44 $stoveX1 = random(20,50);
   45 $microX2 = random(25,55);
   46 $fridgeX2 = random(12,40);
   47 $stoveX2 = random(15,45);
   48 
   49 
   50 BEGIN_TEXT
   51 During the month of January, "ABC Appliances" sold $microA1 microwaves,
   52 $fridgeA1 refrigerators and $stoveA1 stoves, while
   53 "XYZ Appliances" sold $microX1 microwaves,
   54 $fridgeX1 refrigerators and $stoveX1 stoves.
   55 $BR
   56 During the month of February, "ABC Appliances" sold $microA2 microwaves,
   57 $fridgeA2 refrigerators and $stoveA2 stoves, while
   58 "XYZ Appliances" sold $microX2 microwaves,
   59 $fridgeX2 refrigerators and $stoveX2 stoves.
   60 $BR
   61 a) Write a \(2 \times 3 \) matrix summarizing the sales for the month of January. (Keep the
   62 order of information).
   63 
   64 $BCENTER
   65 \{display_matrix([[ans_rule(5),ans_rule(5),ans_rule(5)],
   66 [ans_rule(5),ans_rule(5),ans_rule(5)]], 'align'=>"ccc")
   67 \}
   68 $ECENTER
   69 
   70 b) Write a \(2 \times 3 \) matrix summarizing the sales for the month of February.
   71 (Keep the order of information).
   72 
   73 $BCENTER
   74 \{display_matrix([[ans_rule(5),ans_rule(5),ans_rule(5)],
   75 [ans_rule(5),ans_rule(5),ans_rule(5)]], 'align'=>"ccc")
   76 \}
   77 $ECENTER
   78 
   79 c) Use matrix addition to find  a \(2 \times 3 \) matrix summarizing the total sales for the months of January and February.
   80 
   81 $BCENTER
   82 \{display_matrix([[ans_rule(5),ans_rule(5),ans_rule(5)],
   83 [ans_rule(5),ans_rule(5),ans_rule(5)]], 'align'=>"ccc")
   84 \}
   85 $ECENTER
   86 
   87 END_TEXT
   88 
   89 
   90 ANS(num_cmp($microA1));  ANS(num_cmp($fridgeA1));  ANS(num_cmp($stoveA1));
   91 ANS(num_cmp($microX1));  ANS(num_cmp($fridgeX1));  ANS(num_cmp($stoveX1));
   92 
   93 ANS(num_cmp($microA2));  ANS(num_cmp($fridgeA2));  ANS(num_cmp($stoveA2));
   94 ANS(num_cmp($microX2));  ANS(num_cmp($fridgeX2));  ANS(num_cmp($stoveX2));
   95 $a11 = $microA1 +$microA2;
   96 $a12 = $fridgeA1+$fridgeA2;
   97 $a13 = $stoveA1+ $stoveA2;
   98 $a21 = $microX1 +$microX2;
   99 $a22 = $fridgeX1 + $fridgeX2;
  100 $a23 = $stoveX1+ $stoveX2;
  101 
  102 ANS(num_cmp($a11));  ANS(num_cmp($a12));  ANS(num_cmp($a13));
  103 ANS(num_cmp($a21));  ANS(num_cmp($a22));  ANS(num_cmp($a23));
  104 
  105 ENDDOCUMENT();       # This should be the last executable line in the problem.