Georgia Tech Linear Algebra Problem Addition

Contrib/Georgia Tech/Linear Algebra/Matrix_Numbers_2.pg

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+## 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();