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| 1 : | jjholt | 200 | ## DESCRIPTION |
| 2 : | ## Linear Algebra | ||
| 3 : | ## ENDDESCRIPTION | ||
| 4 : | jj | 144 | |
| 5 : | jjholt | 200 | ## KEYWORDS ('linear algebra','linear system') |
| 6 : | ## Tagged by cmd6a 5/3/06 | ||
| 7 : | |||
| 8 : | ## DBsubject('Linear Algebra') | ||
| 9 : | ## DBchapter('Systems of Linear Equations and Matrices') | ||
| 10 : | ## DBsection('Introduction to Systems of Linear Equations') | ||
| 11 : | ## Date('') | ||
| 12 : | ## Author('') | ||
| 13 : | ## Institution('Rochester') | ||
| 14 : | ## TitleText1('') | ||
| 15 : | ## EditionText1('') | ||
| 16 : | ## AuthorText1('') | ||
| 17 : | ## Section1('') | ||
| 18 : | ## Problem1('') | ||
| 19 : | |||
| 20 : | jj | 144 | DOCUMENT(); # This should be the first executable line in the problem. |
| 21 : | |||
| 22 : | loadMacros( | ||
| 23 : | "PG.pl", | ||
| 24 : | "PGbasicmacros.pl", | ||
| 25 : | "PGchoicemacros.pl", | ||
| 26 : | "PGanswermacros.pl", | ||
| 27 : | "PGgraphmacros.pl", | ||
| 28 : | "PGauxiliaryFunctions.pl" | ||
| 29 : | |||
| 30 : | ); | ||
| 31 : | |||
| 32 : | TEXT(beginproblem()); | ||
| 33 : | $showPartialCorrectAnswers = 1; | ||
| 34 : | |||
| 35 : | $a11 = random(2,6,2) * random(-1,1,2); | ||
| 36 : | $a12 = random(3,5,1) * random(-1,1,2); | ||
| 37 : | $a13 = random(3,5,2) * random(-1,1,2); | ||
| 38 : | $a21 = random(3,5,2) * random(-1,1,2); | ||
| 39 : | $a22 = random(2,6,2) * random(-1,1,2); | ||
| 40 : | $a23 = random(2,6,2) * random(-1,1,2); | ||
| 41 : | $a31 = random(2,6,1) * random(-1,1,2); | ||
| 42 : | $a32 = random(3,5,2) * random(-1,1,2); | ||
| 43 : | $a33 = random(2,6,2) * random(-1,1,2); | ||
| 44 : | |||
| 45 : | $x = random(-5,5,1); | ||
| 46 : | $y = random(-5,5,1); | ||
| 47 : | $z = random(-5,5,1); | ||
| 48 : | |||
| 49 : | $b1 = $a11*$x + $a12*$y + $a13*$z; | ||
| 50 : | $b2 = $a21*$x + $a22*$y + $a23*$z; | ||
| 51 : | $b3 = $a31*$x + $a32*$y + $a33*$z; | ||
| 52 : | |||
| 53 : | $NO_SPACE = '@{}'; | ||
| 54 : | |||
| 55 : | |||
| 56 : | BEGIN_TEXT | ||
| 57 : | |||
| 58 : | Solve the system using matrices (row operations) $BR | ||
| 59 : | \[ \left\{ "\{"; \} | ||
| 60 : | \begin{array}{r${NO_SPACE}r${NO_SPACE}r${NO_SPACE}r${NO_SPACE}r} | ||
| 61 : | $a11 x & +$a12 y & +$a13 z &=& $b1 \cr | ||
| 62 : | $a21 x & +$a22 y & +$a23 z &=& $b2 \cr | ||
| 63 : | $a31 x & +$a32 y & +$a33 z &=& $b3 | ||
| 64 : | \end{array}\right. \] | ||
| 65 : | $BR | ||
| 66 : | \(x = \) \{ans_rule(5)\} | ||
| 67 : | $BR | ||
| 68 : | \(y = \) \{ans_rule(5)\} | ||
| 69 : | $BR | ||
| 70 : | \(z = \) \{ans_rule(5)\} | ||
| 71 : | |||
| 72 : | END_TEXT | ||
| 73 : | ANS(num_cmp($x, mode=>"arith")); | ||
| 74 : | ANS(num_cmp($y, mode=>"arith")); | ||
| 75 : | ANS(num_cmp($z, mode=>"arith")); | ||
| 76 : | |||
| 77 : | ENDDOCUMENT(); # This should be the last executable line in the problem. |
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