diff --git a/Contrib/Georgia Tech/Linear Algebra/Matrix_Numbers_2.pg b/Contrib/Georgia Tech/Linear Algebra/Matrix_Numbers_2.pg new file mode 100644 index 0000000000..335bfa70e8 --- /dev/null +++ b/Contrib/Georgia Tech/Linear Algebra/Matrix_Numbers_2.pg @@ -0,0 +1,165 @@ +## DBsubject(Linear algebra) + +## DBchapter(Matrices) + +## DBsection(Echelon form) + +## Institution(Georgia Institute of Technology) + +## Author(Gregory Mayer and Jake Abujawdeh) + +## Level(2) + +## MO(1) + +## TitleText1('Linear Algebra and its Applications') + +## AuthorText1('Lay') + +## EditionText1('5e') + +## Section1('1.2') + +## Problem1('13') + +## KEYWORDS('Echelon form', 'matrices') + + + +DOCUMENT(); + +loadMacros( +"PGstandard.pl", +"MathObjects.pl", +"PGcourse.pl", +"PGcourse.pl", +"answerHints.pl", +"scaffold.pl", +"PGchoicemacros.pl", +); + + + +TEXT(beginproblem()); + + +Context("Numeric"); + + + + +$b = 7; + + + + + + + + + + + + + + + +Context()->texStrings; +BEGIN_TEXT +$BR +Matrix \(A\) is \(2 \times 3\), is in RREF, has a pivot in every row, and every entry of \(A\) is either 1 or 0. How many different matrices can you construct that meet all of these criteria? \{ans_rule(5)\} + + + +$BR +$BR + + + +END_TEXT +Context()->normalStrings; + +################################### +# Answers + +$showPartialCorrectAnswers = 1; + + + + +ANS(num_cmp($b)); + + + + +COMMENT('MathObject version.'); + + +BEGIN_SOLUTION +There are seven matrices that furfill the requirements: +$BR +$BR +\[\left(\begin{array}{cc} + 1 & 0 & 0 \cr + 0 & 1 & 0 + \end{array}\right) \] + +$BR +$BR +\[\left(\begin{array}{cc} + 1 & 0 & 1 \cr + 0 & 1 & 0 + \end{array}\right) \] + + +$BR +$BR +\[\left(\begin{array}{cc} + 1 & 0 & 0 \cr + 0 & 1 & 1 + \end{array}\right) \] + +$BR +$BR +\[\left(\begin{array}{cc} + 1 & 0 & 1 \cr + 0 & 1 & 1 + \end{array}\right) \] + +$BR +$BR +\[\left(\begin{array}{cc} + 1 & 0 & 0 \cr + 0 & 0 & 1 + \end{array}\right) \] + +$BR +$BR +\[\left(\begin{array}{cc} + 1 & 1 & 0 \cr + 0 & 0 & 1 + \end{array}\right) \] + + +$BR +$BR +\[\left(\begin{array}{cc} + 0 & 1 & 0 \cr + 0 & 0 & 1 + \end{array}\right) \] + + + +END_SOLUTION + + + + + + + + + + + +ENDDOCUMENT();