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| 1 : | jj | 61 | ##DESCRIPTION |
| 2 : | ##KEYWORDS('') | ||
| 3 : | ## | ||
| 4 : | ##ENDDESCRIPTION | ||
| 5 : | |||
| 6 : | DOCUMENT(); # This should be the first executable line in the problem. | ||
| 7 : | |||
| 8 : | loadMacros( | ||
| 9 : | "PGasu.pl", | ||
| 10 : | "PG.pl", | ||
| 11 : | "PGbasicmacros.pl", | ||
| 12 : | "PGchoicemacros.pl", | ||
| 13 : | "PGanswermacros.pl", | ||
| 14 : | "PGauxiliaryFunctions.pl", | ||
| 15 : | "PGmatrixmacros.pl" | ||
| 16 : | ); | ||
| 17 : | |||
| 18 : | TEXT(&beginproblem); | ||
| 19 : | $showPartialCorrectAnswers = 1; | ||
| 20 : | |||
| 21 : | $a1 = non_zero_random(-9,9,1); | ||
| 22 : | $b1 = non_zero_random(-99,99,1); | ||
| 23 : | $c1 = non_zero_random(-99,99,1); | ||
| 24 : | $d1 = random(-99,99,1); | ||
| 25 : | $a2 = 0; | ||
| 26 : | $b2 = non_zero_random(-99,99,1); | ||
| 27 : | $c2 = non_zero_random(-9,9,1); | ||
| 28 : | $d2 = random(-9,9,1); | ||
| 29 : | $a3 = non_zero_random(-99,99,1); | ||
| 30 : | $b3 = 0; | ||
| 31 : | $c3 = random(2,99,1); | ||
| 32 : | $d3 = random(-99,99,1); | ||
| 33 : | $a4 = random(-9,9,1); | ||
| 34 : | $b4 = non_zero_random(-9,9,1); | ||
| 35 : | $c4 = non_zero_random(-99,99,1); | ||
| 36 : | $d4 = random(-99,99,1); | ||
| 37 : | $a5 = random(2,99,1); | ||
| 38 : | $b5 = random(1,99,1); | ||
| 39 : | $c5 = 0; | ||
| 40 : | $d5 = random(-9,9,1); | ||
| 41 : | |||
| 42 : | @a = ($a1, $a2, $a3, $a4, $a5); | ||
| 43 : | @b = ($b1, $b2, $b3, $b4, $b5); | ||
| 44 : | @c = ($c1, $c2, $c3, $c4, $c5); | ||
| 45 : | @d = ($d1, $d2, $d3, $d4, $d5); | ||
| 46 : | |||
| 47 : | @mx = ("$a1 x", "", "$a3 x", "$a4 x", "$a5 x"); | ||
| 48 : | @my = ("+$b1 y", "+$b2 y", "", "+$b4 y", "+$b5 y"); | ||
| 49 : | @mz = ("+$c1 z", "+$c2 z", "+$c3 z", "+$c4 z", ""); | ||
| 50 : | @m = ("$d1", "$d2", "$d3", "$d4", "$d5"); | ||
| 51 : | |||
| 52 : | $tag1 = random(0,2,1); | ||
| 53 : | $tag2 = $tag1 +1; | ||
| 54 : | $tag3 = $tag1 +2; | ||
| 55 : | |||
| 56 : | $NO_SPACE = '@{}'; | ||
| 57 : | |||
| 58 : | BEGIN_TEXT | ||
| 59 : | |||
| 60 : | Write the augmented matrix of the system | ||
| 61 : | \[ \left\{"\{"\} \begin{array}{r${NO_SPACE}r${NO_SPACE}r${NO_SPACE}r${NO_SPACE}r} | ||
| 62 : | \{join("&",$mx[$tag1],$my[$tag1],$mz[$tag1],"=",$m[$tag1] ) \} \cr | ||
| 63 : | \{join("&",$mx[$tag2],$my[$tag2],$mz[$tag2],"=",$m[$tag2] ) \} \cr | ||
| 64 : | \{join("&",$mx[$tag3],$my[$tag3],$mz[$tag3],"=",$m[$tag3] ) \} \cr | ||
| 65 : | \end{array} \right. \] | ||
| 66 : | |||
| 67 : | $BR | ||
| 68 : | |||
| 69 : | $BCENTER | ||
| 70 : | \{display_matrix([[ans_rule(5),ans_rule(5),ans_rule(5),ans_rule(5)], | ||
| 71 : | [ans_rule(5),ans_rule(5),ans_rule(5),ans_rule(5)], | ||
| 72 : | [ans_rule(5),ans_rule(5),ans_rule(5),ans_rule(5)]], | ||
| 73 : | 'align' =>"ccc|c") | ||
| 74 : | \} | ||
| 75 : | $ECENTER | ||
| 76 : | |||
| 77 : | |||
| 78 : | END_TEXT | ||
| 79 : | |||
| 80 : | |||
| 81 : | |||
| 82 : | &ANS(arith_num_cmp($a[$tag1])); | ||
| 83 : | &ANS(arith_num_cmp($b[$tag1])); | ||
| 84 : | &ANS(arith_num_cmp($c[$tag1])); | ||
| 85 : | &ANS(arith_num_cmp($d[$tag1])); | ||
| 86 : | |||
| 87 : | # row 2 | ||
| 88 : | &ANS(arith_num_cmp($a[$tag2])); | ||
| 89 : | &ANS(arith_num_cmp($b[$tag2])); | ||
| 90 : | &ANS(arith_num_cmp($c[$tag2])); | ||
| 91 : | &ANS(arith_num_cmp($d[$tag2])); | ||
| 92 : | |||
| 93 : | # row 3 | ||
| 94 : | &ANS(arith_num_cmp($a[$tag3])); | ||
| 95 : | &ANS(arith_num_cmp($b[$tag3])); | ||
| 96 : | &ANS(arith_num_cmp($c[$tag3])); | ||
| 97 : | &ANS(arith_num_cmp($d[$tag3])); | ||
| 98 : | |||
| 99 : | |||
| 100 : | |||
| 101 : | ENDDOCUMENT(); # This should be the last executable line in the problem. |
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