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# Annotation of /trunk/NationalProblemLibrary/ASU-topics/set119LinearSystems/p21.pg

 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.