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| 1 : | jjholt | 101 | ## DESCRIPTION |
| 2 : | ## Matrix Algebra | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | |||
| 5 : | ## KEYWORDS('Algebra' 'Matrix' 'Matrices') | ||
| 6 : | ## Tagged by tda2d | ||
| 7 : | |||
| 8 : | ## DBsubject('Algebra') | ||
| 9 : | jjholt | 483 | ## DBchapter('Systems of Equations and Inequalities') |
| 10 : | ## DBsection('The Algebra of Matrices') | ||
| 11 : | jjholt | 101 | ## Date('') |
| 12 : | ## Author('') | ||
| 13 : | ## Institution('ASU') | ||
| 14 : | ## TitleText1('') | ||
| 15 : | ## EditionText1('') | ||
| 16 : | ## AuthorText1('') | ||
| 17 : | ## Section1('') | ||
| 18 : | ## Problem1('') | ||
| 19 : | |||
| 20 : | jj | 61 | 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 : | gage | 268 | TEXT(beginproblem()); |
| 34 : | jj | 61 | |
| 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() ; |
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