a) I was confirming that the matrix checker for parametric solutions would allow any multiple of the basis element for the solution of the associated homogeneous system. I entered the result one would get automatically from row reduction, but then tried another correct answer.

The answer preview used the first component of the basis vector from my new answer, but the other three components were from my previous answer. See the attached image.

b) I added a second part to the question that asks for the parametric solution to the homogeneous system associated with the nonhomogeneous system in the first part of the question. I cannot seem to get the answer checker to work here and I am assuming it is because of a programming error.

The error I get when I enter the correct solution is "Coordinate of vector cannot be a matrix".

The code is below.

## DESCRIPTION

## Linear Algebra

## ENDDESCRIPTION

## Tagged by cmd6a 5/3/06

## DBsubject(Linear algebra)

## DBchapter(Systems of linear equations)

## DBsection(Systems with 4 or more variables)

## Date(July 2013)

## Institution(Rochester and Hope College)

## Author(Paul Pearson)

## MLT(AlmostRREFSolnWithParams)

## MLTleader(1)

## Level(2)

## MO(1)

## TitleText1('Linear Algebra with Applications')

## AuthorText1('Jeffrey Holt')

## EditionText1('1')

## Section1('2.1')

## Problem1('')

# Revised by MEWaggoner 2/10/2015

DOCUMENT();

loadMacros(

"PGstandard.pl",

"MathObjects.pl",

"parserMultiAnswer.pl",

"MatrixCheckers.pl",

"PGcourse.pl",

);

TEXT(beginproblem());

$showPartialCorrectAnswers = 1;

Context('Matrix');

$a = non_zero_random(-5,5,1);

$c = non_zero_random(-5,5,1);

$b = non_zero_random(-5,5,1);

$d = $a - $b + $c;

$NO_SPACE = '@{}';

$displace = Matrix([$a - $b + $c, $b - $c, $c, 0])->transpose;

$basis1 = Matrix([- 1, 1, -1, 1])->transpose;

$multians1 = MultiAnswer($displace, $basis1)->with(

singleResult => 1,

separator => ', ',

tex_separator => ', ',

allowBlankAnswers=>0,

checker => ~~¶metric_plane_checker_columns,

);

$multians2 = MultiAnswer($basis1)->with(

singleResult => 1,

separator => ', ',

tex_separator => ', ',

allowBlankAnswers=>0,

checker => ~~&basis_checker_one_column,

);

Context()->texStrings;

BEGIN_TEXT

Part 1: Solve the nonhomogeneous system

\[ \left\lbrace \begin{array}{r${NO_SPACE}r${NO_SPACE}r${NO_SPACE}r${NO_SPACE}r${NO_SPACE}r}

x_1 & + x_2 & & & = & $a \\

& x_2 & + x_3 & & = & $b \\

& & x_3 & + x_4 & = & $c \\

x_1 & & & + x_4 & = & $d

\end{array} \right. \]

$BR

\(

\displaystyle

\left\lbrack

\begin{array}{c}

x_1 \\

x_2 \\

x_3 \\

x_4

\end{array}

\right\rbrack

= \)

\{ $multians1->ans_array \}

\( + s \)

\{ $multians1->ans_array \}.

$PAR

$PAR

Part 2: Based on your results for the solution of the nonhomogeneous equation above, solve the associated homogeneous equation (you should be able to answer this without any further work.)

\[ \left\lbrace \begin{array}{r${NO_SPACE}r${NO_SPACE}r${NO_SPACE}r${NO_SPACE}r${NO_SPACE}r}

x_1 & + x_2 & & & = & 0 \\

& x_2 & + x_3 & & = & 0 \\

& & x_3 & + x_4 & = & 0 \\

x_1 & & & + x_4 & = & 0

\end{array} \right. \]

$BR

\(

\displaystyle

\left\lbrack

\begin{array}{c}

x_1 \\

x_2 \\

x_3 \\

x_4

\end{array}

\right\rbrack

= s \)

\{ $multians2->ans_array \}.

END_TEXT

Context()->normalStrings;

ANS($multians1->cmp);

ANS($multians2->cmp);

COMMENT('MathObject version');

ENDDOCUMENT();