** Using WeBWorK **

## DESCRIPTION
## Linear Algebra: Matrices (Math 1410)
## ENDDESCRIPTION

## DBsubject(Linear Algebra)
## DBchapter(Matrices)
## DBsection()
## Date(2017-06-15)
## Institution(University of Lethbridge)
## Authors(Olivia Henders & Nicole Wilson)
## MO(1)
## KEYWORDS('linear algebra', 'matrices')


##############################
# Initialization

DOCUMENT();

loadMacros(
 "PGstandard.pl",
 "MathObjects.pl",
 "AnswerFormatHelp.pl",
 "PGML.pl",
 "parserRadioButtons.pl"
);

TEXT(beginproblem());


#############################
# Setup

$showPartialCorrectAnswers = 1;
$showDimensionHints => 1;

Context("Vector");
# Column vector that will be used for vector-matrix operations.
$v = ColumnVector(0,3,-2);

Context("Matrix")->variables->are(t=>"Real");

# Matrix setup. $A is statically defined 2x3,
# $B is 3x3 with randomly determined entries,
# $C is 2x3 with randomly determined entries and two variables,
# and $I is the 3x3 identity matrix

$A = Matrix([[1,2,3],[4,5,6]]);
$B = Matrix([
[random(-5,5,1),random(-5,5,1),random(-5,5,1)],
[random(-5,5,1),random(-5,5,1),random(-5,5,1)],
[random(-5,5,1),random(-5,5,1),random(-5,5,1)]
]);

# Have to generate the coefficients here so they can be used separately.
$C1_2 = Compute("3");
$C2_2 = non_zero_random(-5,5);

$C = Matrix([
[random(-5,5,1),"$C1_2 t",random(-5,5,1)],
[random(-5,5,1),"$C2_2 t",random(-5,5,1)]
]);

$D = Matrix([[3,5],[1,2]]);

$E = Matrix([[5],[7],[3]]);

$I = Value::Matrix->I(3);

# Generate the matrix pieces that include variables here so that they can be
# turned into variable objects when in the matrix.
$answerA1_2 = $A->element(1,2) - Formula("$C1_2 t");
$answerA2_2 = $A->element(2,2) - Formula("$C2_2 t");
$answerA = Matrix([
 [($A->element(1,1) - $C->eval(t=>1)->element(1,1)), Formula($answerA1_2)->reduce, ($A->element(1,3) - $C->eval(t=>1)->element(1,3))],
 [($A->element(2,1) - $C->eval(t=>1)->element(2,1)), Formula($answerA2_2)->reduce, ($A->element(2,3) - $C->eval(t=>1)->element(2,3))]
]);
$answerB = Compute("DNE");
$answerC = Matrix($A * $B);

# Generate the matrix pieces that include variables here so that they can be
# turned into variable objects when in the matrix.
$answerD1_1 = ($C->eval(t=>1)->element(1,1) * $B->element(1,1)) + (Formula("$C1_2 t") * $B->element(2,1)) + ($C->eval(t=>1)->element(1,3) * $B->element(3,1));
$answerD1_2 = ($C->eval(t=>1)->element(1,1) * $B->element(1,2)) + (Formula("$C1_2 t") * $B->element(2,2)) + ($C->eval(t=>1)->element(1,3) * $B->element(3,2));
$answerD1_3 = ($C->eval(t=>1)->element(1,1) * $B->element(1,3)) + (Formula("$C1_2 t") * $B->element(2,3)) + ($C->eval(t=>1)->element(1,3) * $B->element(3,3));
$answerD2_1 = ($C->eval(t=>1)->element(2,1) * $B->element(1,1)) + (Formula("$C2_2 t") * $B->element(2,1)) + ($C->eval(t=>1)->element(2,3) * $B->element(3,1));
$answerD2_2 = ($C->eval(t=>1)->element(2,1) * $B->element(1,2)) + (Formula("$C2_2 t") * $B->element(2,2)) + ($C->eval(t=>1)->element(2,3) * $B->element(3,2));
$answerD2_3 = ($C->eval(t=>1)->element(2,1) * $B->element(1,3)) + (Formula("$C2_2 t") * $B->element(2,3)) + ($C->eval(t=>1)->element(2,3) * $B->element(3,3));
$answerD = Matrix([
 [Formula($answerD1_1)->reduce, Formula($answerD1_2)->reduce, Formula($answerD1_3)->reduce],
 [Formula($answerD2_1)->reduce, Formula($answerD2_2)->reduce, Formula($answerD2_3)->reduce]
]);
$answerE = Matrix($I + $B);
$answerF = Matrix($B**2);
$answerG = $B * $I;
$answerH = $A->transpose;
$answerI = $D->inverse;
$answerJ = $B->det;
$answerK = $A->row(2);
$answerL = $A->column(1);
$answerM = $A->element(1,3);
$answerN = List($C->eval(t=>1)->dimensions);
$answerO = $A * ColumnVector($v);
$answerP = Vector($B->row(1));
$answerQ = Vector($B->column(1));
$answerR = $B->proj($E);

if ($B->isZero)
{
 $answerS = RadioButtons([True, False], True);
}
else
{
 $answerS = RadioButtons([True, False], False);
}

if ($B->isOne)
{
 $answerT = RadioButtons([True, False], True);
}
else
{
 $answerT = RadioButtons([True, False], False);
}

if ($D->isSquare)
{
 $answerU = RadioButtons([True, False], True);
}
else
{
 $answerU = RadioButtons([True, False], False);
}

if ($D->isRow)
{
 $answerV = RadioButtons([True, False], True);
}
else
{
 $answerV = RadioButtons([True, False], False);
}

if ($B->is_symmetric)
{
 $answerW = RadioButtons([True, False], True);
}
else
{
 $answerW = RadioButtons([True, False], False);
}

$answerX = $B->norm_one;
$answerY = $B->norm_max;
$answerZ = $B->kleene;
$answerAi = $B->normalize($v);
$answerBi = $D->decompose_LR;
$answerCi = $A->L;
$answerDi = $A->R;
$answerEi = $B->PL;
$answerFi = $B->PR;
$answerGi = $D->solve_LR($v);
$answerHi = $B->condition($B->inverse);
$answerIi = $D->order_LR;
$answerJi = $B->solve_GSM();
$answerKi = $B->solve_SSM();
$answerLi = $B->solve_RM();

##############################
# Problem Text...