## DESCRIPTION ## Linear Algebra ## ENDDESCRIPTION ## KEYWORDS ('linear algebra','linear system') ## Tagged by cmd6a 5/3/06 ## DBsubject('Linear Algebra') ## DBchapter('Systems of Linear Equations and Matrices') ## DBsection('Introduction to Systems of Linear Equations') ## Date('') ## Author('') ## Institution('Rochester') ## TitleText1('') ## EditionText1('') ## AuthorText1('') ## Section1('') ## Problem1('') DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGgraphmacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(beginproblem()); $showPartialCorrectAnswers = 1;$a11 = random(2,6,2) * random(-1,1,2); $a12 = random(3,5,1) * random(-1,1,2);$a13 = random(3,5,2) * random(-1,1,2); $a21 = random(3,5,2) * random(-1,1,2);$a22 = random(2,6,2) * random(-1,1,2); $a23 = random(2,6,2) * random(-1,1,2);$a31 = random(2,6,1) * random(-1,1,2); $a32 = random(3,5,2) * random(-1,1,2);$a33 = random(2,6,2) * random(-1,1,2); $x = random(-5,5,1);$y = random(-5,5,1); $z = random(-5,5,1);$b1 = $a11*$x + $a12*$y + $a13*$z; $b2 =$a21*$x +$a22*$y +$a23*$z;$b3 = $a31*$x + $a32*$y + $a33*$z; $NO_SPACE = '@{}'; BEGIN_TEXT Solve the system using matrices (row operations)$BR $\left\{ "\{"; \} \begin{array}{r{NO_SPACE}r{NO_SPACE}r{NO_SPACE}r{NO_SPACE}r} a11 x & +a12 y & +a13 z &=& b1 \cr a21 x & +a22 y & +a23 z &=& b2 \cr a31 x & +a32 y & +a33 z &=& b3 \end{array}\right.$ $BR $$x =$$ \{ans_rule(5)\}$BR $$y =$$ \{ans_rule(5)\} $BR $$z =$$ \{ans_rule(5)\} END_TEXT ANS(num_cmp($x, mode=>"arith")); ANS(num_cmp($y, mode=>"arith")); ANS(num_cmp($z, mode=>"arith")); ENDDOCUMENT(); # This should be the last executable line in the problem.