## DESCRIPTION ## Linear Algebra ## ENDDESCRIPTION ## KEYWORDS('bases' 'basis' 'matrix' 'linearly independent') ## Tagged by tda2d ## DBsubject('Linear Algebra') ## DBchapter('Vector Spaces') ## DBsection('Bases') ## Date('') ## Author('modified by Shifrin') ## Institution('TCNJ') ## 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", "PGmatrixmacros.pl", "PGnumericalmacros.pl", "PGauxiliaryFunctions.pl", "PGmorematrixmacros.pl", "MathObjects.pl" ); TEXT(beginproblem()); $showPartialCorrectAnswers = 1; Context("Vector");$x = ColumnVector(-2,3,0); $y = ColumnVector(6,-1,5); # Make a new checkbox multiple choice$cmc1 = new_checkbox_multiple_choice(); # $cmc now "contains" the checkbox multiple choice object. # Insert some questions and matching answers in the q/a list$cmc1 -> qa ( "Determine if $$W$$ is a basis for $${\mathbb R}^3$$ and check the correct answer(s) below.", " $$W$$ is not a basis because it does not span $${\mathbb R}^3$$.", ); # Insert some incorrect answers $cmc1 -> extra( " $$W$$ is a basis.", " $$W$$ is not a basis because it is linearly dependent.", ); Context()->texStrings; BEGIN_TEXT Let $$W$$ be the set $$\left\{"\{"\} x, y \right\}$$.$PAR \{$cmc1 -> print_q \}$BR \{$cmc1 -> print_a \} END_TEXT ANS(checkbox_cmp($cmc1->correct_ans ) ) ; ENDDOCUMENT(); # This should be the last executable line in the problem.