View of /trunk/NationalProblemLibrary/ASU-topics/set119MatrixAlgebra/p15.pg

    1 ## DESCRIPTION
    2 ## Matrix Algebra
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Algebra' 'Matrix' 'Matrices')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Algebra')
    9 ## DBchapter('Linear Algebra')
   10 ## DBsection('Matrix Algebra')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('ASU')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT() ;
   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 
   33 TEXT(&beginproblem);
   34 
   35 
   36 $c = random(-6,6);
   37 do {$d = non_zero_random(-4,4);} until ($d != $c);
   38 $e = random(2,6);
   39 do {$f = non_zero_random(-4,4);} until ($f != $e);
   40 $g = random(-5,5);
   41 do {$h = random(-4,4);} until ($g != $h);
   42 
   43 
   44 $showPartialCorrectAnswers = 1 ;
   45 
   46 BEGIN_TEXT
   47 Perform the following operation:
   48 
   49 \[ \{display_matrix_mm([['a' , '1-a' ],[
   50 '1+a' , '-a' ]]) \}
   51 \{ display_matrix_mm(
   52 [[$c      , $e , $g ],
   53 [$d , $f        , $h ]], align=>'rrr') \}
   54  \]
   55 $BR$BR
   56 $BCENTER
   57 \{ mbox('\(=\)', display_matrix([[ans_rule(10),ans_rule(10),ans_rule(10)],
   58 [ans_rule(10),ans_rule(10),ans_rule(10)]],
   59 'align'=>"ccc"))
   60 \}
   61 $ECENTER
   62 
   63 $BR
   64 $BBOLD Note: $EBOLD The entries in the resulting matrix are functions of
   65 \(a \).
   66 END_TEXT
   67 
   68 
   69 $a11="($c-$d)*a+$d";
   70 $a12="($e-$f)*a+$f";
   71 $a13="($g-$h)*a+$h";
   72 $a21="($c-$d)*a+$c";
   73 $a22="($e-$f)*a+$e";
   74 $a23="($g-$h)*a+$g";
   75 
   76 ANS(fun_cmp("$a11",var=>'a'));
   77 ANS(fun_cmp("$a12",var=>'a'));
   78 ANS(fun_cmp("$a13",var=>'a'));
   79 ANS(fun_cmp("$a21",var=>'a'));
   80 ANS(fun_cmp("$a22",var=>'a'));
   81 ANS(fun_cmp("$a23",var=>'a'));
   82 
   83 
   84 
   85 ENDDOCUMENT() ;