Merge pull request #1156 from gajennings/main

Fix bug 4828, use MathObjects, PGML, add solution

Author: gajennings

OpenProblemLibrary/Rochester/setLinearAlgebra19QRfactorization/ur_la_19_1.pg

@@ -23,50 +23,59 @@ DOCUMENT();        # This should be the first executable line in the problem.
 loadMacros(
   "PGstandard.pl",
   "MathObjects.pl",
+  "PGML.pl",
+  "parserMultiAnswer.pl",
   "PGcourse.pl"
 );
 
-TEXT(beginproblem());
 $showPartialCorrectAnswers = 1;
 
 Context('Matrix');
 
-$norm = 0;
+$normsq = 0;
 
-foreach $i (1..3) {
+foreach $i (0..2) {
 	$myq[$i] = non_zero_random(-3,3,1);
-	$norm = $norm + $myq[$i] * $myq[$i];
+	$normsq = $normsq + $myq[$i] * $myq[$i];
 }
 
-$myQ = Matrix([ [$myq[1]], [$myq[2]], [$myq[3]] ]);
+$norm = sqrt($normsq);
 
-$norm = sqrt($norm);
+$mult = non_zero_random(1,5,1);
 
-$myR = Matrix([non_zero_random(1,5,1)]);
+$Q = Matrix([[$myq[0]],[$myq[1]],[$myq[2]]])/$norm;
 
-$M = $myQ * $myR;
+$R = Matrix([[$norm*$mult]]);
 
-foreach $i (1..3) {
-        $q[$i] = $myq[$i]/$norm;
-}
+$M = Matrix([[$myq[0]],[$myq[1]],[$myq[2]]])*$mult;
+
+$multAns = MultiAnswer($Q,$R)->with(
+  singleResult => 1,
+  checker      => sub {
+    my ($correct, $student, $self) = @_;
+    my ($Qstu, $Rstu) = @{$student};
+    my ($Qcor,    $Rcor)    = @{$correct};
+    if ( ($Qstu == $Qcor && $Rstu == $Rcor) or 
+         ($Qstu == -$Qcor && $Rstu == -$Rcor) ) 
+      { return 1; }
+    else { return 0;}
+  }
+);
 
-$Q = Matrix([ [$q[1]], [$q[2]], [$q[3]] ]);
+BEGIN_PGML
+Find the QR factorization of the given matrix.
 
-$R = $myR * $norm;
+[``[$M] = ``] [_____]*{$multAns} [_____]*{$multAns} 
+END_PGML
 
-Context()->texStrings;
-BEGIN_TEXT
-Find the \(QR\) factorization of the given matrix.
-$BR 
-$BR
-$BCENTER
-\($M = \) \{ $Q->ans_array \} \{ $R->ans_array \} 
-$ECENTER
-END_TEXT
-Context()->normalStrings;
+BEGIN_PGML_SOLUTION
+The [`3\times 1`] matrix M is equivalent to a vector and Q is supposed to be an orthogonal matrix, that is, a sequence of orthonormal column vectors, so Q is equivalent to a single unit vector that is parallel to M.  The length of M is [`[$mult]\sqrt{[$normsq]}`]
+so      
+    [``Q = (\pm M)\big(\frac{1}{[$mult]\sqrt{[$normsq]}}\big)``]
+and 
+    [``R = \pm [$mult]\sqrt{[$normsq]} ``] 
+with the same plus or minus sign for both.
+END_PGML_SOLUTION
 
-ANS($Q->cmp);
-ANS($R->cmp);
-;
 ENDDOCUMENT();       # This should be the last executable line in the problem.