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Merge pull request #1275 from gajennings/main
Fix issue #1270, update to PGML
2 parents 8806d67 + 26751a1 commit b28e69f

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‎OpenProblemLibrary/Hope/Multi1/03-03-Span/Graphical_01/Graphical_01.pg‎

Lines changed: 45 additions & 76 deletions
Original file line numberDiff line numberDiff line change
@@ -2,7 +2,6 @@
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## Linear Algebra
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## ENDDESCRIPTION
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5-
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## DBsubject(Linear algebra)
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## DBchapter(Euclidean spaces)
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## DBsection(Linear independence)
@@ -11,24 +10,24 @@
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## Level(3)
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## MO(1)
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## KEYWORDS('linear algebra','vector space','subspaces')
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## RESOURCES('basis-2d.png','basis-3d.png','linearly-dependent-2d.png','linearly-dependent-not-spanning-3d.png','linearly-dependent-spanning-3d.png','linearly-independent-not-spanning-3d.png")## Date(July 2013')
13+
## RESOURCES('basis-2d.png','basis-3d.png','linearly-dependent-2d.png','linearly-dependent-not-spanning-3d.png','linearly-dependent-spanning-3d.png','linearly-independent-not-spanning-3d.png")
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## Date(July 2013')
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DOCUMENT();
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loadMacros(
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"PGstandard.pl",
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"MathObjects.pl",
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"PGchoicemacros.pl",
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"PGML.pl",
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"parserPopUp.pl",
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"unionTables.pl",
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"niceTables.pl",
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"PGcourse.pl"
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);
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install_problem_grader(~~&std_problem_grader);
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$showPartialCorrectAnswers = 0;
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$refreshCachedImages = 1;
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TEXT(beginproblem());
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Context('Matrix');
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Context("Numeric");
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# six graphics files
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@files = (
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"basis-2d.png",
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"basis-3d.png",
@@ -38,86 +37,56 @@ Context('Matrix');
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"linearly-independent-not-spanning-3d.png",
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);
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#convert files to figures
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@fig = ();
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foreach my $i (0..$#files) {
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$fig[$i] = image($files[$i],width=>200,height=>200,tex_size=>320);
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foreach my $file (@files) {
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push @fig, image($file,width=>200,height=>200,tex_size=>320);
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}
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@indep = (
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"linearly independent",
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"linearly independent",
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"linearly dependent",
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"linearly dependent",
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"linearly dependent",
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"linearly independent",
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);
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#labels (see problem text) of corresponding descriptions of the six files
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@labels = ("A","D","A","A","D","C");
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@popup_indep = ();
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foreach my $i (0..$#indep) {
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$popup_indep[$i] = PopUp(['choose','linearly dependent','linearly independent'],$indep[$i]);
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#six corresponding answer pop ups
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@ans=();
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foreach my $label (@labels){
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push @ans, PopUp(["??","A","B","C","D"],$label);
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}
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@span = (
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"R^2",
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"R^3",
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"R^2",
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"a 2d plane through the origin inside R^3",
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"R^3",
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"a 2d plane through the origin inside R^3",
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#scramble the answers and figures in the same way
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@slice = random_subset(6,(0..5));
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@fig = @fig[@slice];
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@ans = @ans[@slice];
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$table = LayoutTable(
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[ [$fig[0], $fig[1], $fig[2] ],
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[$ans[0]->menu(), $ans[1]->menu(), $ans[2]->menu() ],
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[ $fig[3], $fig[4], $fig[5] ],
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[$ans[3]->menu(),$ans[4]->menu(),$ans[5]->menu() ]
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]
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);
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@popup_span = ();
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foreach my $i (0..$#span) {
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$popup_span[$i] = PopUp(['choose','a line through the origin inside R^2',"R^2","a 2d plane through the origin inside R^3","R^3",],$span[$i]);
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}
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BEGIN_PGML
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A set of two, three, or four red vectors in [``\mathbb{R}^2``] or [``\mathbb{R}^3``] is shown in each figure below. Below the six figures is a list of four descriptions, labeled [`A,\cdots,D`], that may describe the *span* of the vectors in the figures. In the selection box below each figure choose the letter of the description that matches the figure. *Note:* For pictures in [``\mathbb{R}^3 ``], a grid is drawn in the [`xy`]-plane, and vectors with their tip on the grid are in the [`xy`]-plane, while vectors with their tip not on the grid are not in the \(xy\)-plane.
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@basis = (
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"basis",
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"basis",
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"not a basis",
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"not a basis",
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"not a basis",
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"not a basis",
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);
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[@ $table @]*
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@popup_basis = ();
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foreach my $i (0..$#indep) {
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$popup_basis[$i] = PopUp(['choose','basis','not a basis'],$basis[$i]);
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}
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Descriptions
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@perm = shuffle(scalar(@files));
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@fig = @fig[@perm];
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@popup_indep = @popup_indep[@perm];
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@popup_span = @popup_span[@perm];
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@popup_basis = @popup_basis[@perm];
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Context()->texStrings;
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BEGIN_TEXT
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A set of two, three, or four red vectors in \( \mathbb{R}^2 \) or \( \mathbb{R}^3 \) is shown in each picture below.
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Choose the correct description of the span of each set of vectors.
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Note: For the pictures in \( \mathbb{R}^3 \), a grid is drawn in the \(xy\)-plane, and vectors
103-
with their tip on the grid are in the \(xy\)-plane, while vectors with their tip not on the grid are
104-
not in the \(xy\)-plane.
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\{
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BeginTable().
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AlignedRow([$fig[0],$fig[1],$fig[2]]).
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TableSpace(5,0).
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AlignedRow([$popup_span[0]->menu,$popup_span[1]->menu,$popup_span[2]->menu]).
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TableSpace(25,6).
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AlignedRow([$fig[3],$fig[4],$fig[5]]).
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TableSpace(5,0).
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AlignedRow([$popup_span[3]->menu,$popup_span[4]->menu,$popup_span[5]->menu]).
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EndTable();
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\}
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END_TEXT
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Context()->normalStrings;
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119-
foreach my $i (0..$#popup_span) {
120-
ANS( $popup_span[$i]->cmp );
121-
}
76+
A. The vectors span [``\mathbb{R}^2``].
77+
78+
B. The vectors span a line through the origin inside [``\mathbb{R}^2``].
79+
80+
C. The vectors span a 2-dimensional plane through the origin inside [``\mathbb{R}^3``] but the plane is not [``\mathbb{R}^2``].
81+
82+
D. The vectors span [``\mathbb{R}^3``].
83+
END_PGML
84+
85+
ANS($ans[0]->cmp());
86+
ANS($ans[1]->cmp());
87+
ANS($ans[2]->cmp());
88+
ANS($ans[3]->cmp());
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ANS($ans[4]->cmp());
90+
ANS($ans[5]->cmp());
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ENDDOCUMENT();

‎OpenProblemLibrary/Hope/Multi1/03-03-Span/Graphical_01/basis-3d.png‎

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