webwork-open-problem-library/Contrib/BentleyUniversity/MathematicsOfComputerGraphics/setMoCG-Ch5/5-10-MatrixMultiplicationWithVariables.pg at 5b81d053600776c4338fd7c5c39927c53f8d10da · openwebwork/webwork-open-problem-library · GitHub

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## DESCRIPTION
## Matrix multiplication problems with variable entries
## ENDDESCRIPTION

## DBsubject(Linear Algebra)
## DBchapter(Matrices)
## DBsection(Matrix Algebra)
## Date(02/02/2018)
## Institution(Bentley University)
## Author(Nathan Carter)
## TitleText1('Introduction to the Mathematics of Computer Graphics')
## AuthorText1('Nathan Carter')
## EditionText1('1')
## Section1('5')
## Problem1('10')
## KEYWORDS('matrices','matrix multiplication')

DOCUMENT();
loadMacros(
  "PGstandard.pl",
  "MathObjects.pl",
  "PGML.pl",
  "PGcourse.pl",

  "PGessaymacros.pl",
);

Context("Matrix");
Context()->variables->add( u => Real );
Context()->variables->add( v => Real );
Context()->variables->add( w => Real );
Context()->variables->add( a => Real );
Context()->variables->add( b => Real );
Context()->variables->add( c => Real );
Context()->variables->add( d => Real );
Context()->variables->add( e => Real );
$showPartialCorrectAnswers = 1;
$L3 = Matrix( [
    [ Formula( list_random( 0, 1, "a", "b", "c" ) ),
      Formula( list_random( 0, 1, "a", "b", "c" ) ),
      Formula( list_random( 0, 1, "a", "b", "c" ) ) ],
    [ Formula( list_random( "a", "b", "c" ) ),
      Formula( list_random( "a", "b", "c" ) ),
      Formula( list_random( 0, 1, "a", "b", "c" ) ) ],
    [ 0, 0, 1 ]
] );
$R3 = Matrix( [
    [ Formula( list_random( 0, 1, "d", "e" ) ),
      Formula( list_random( 0, 1, "d", "e" ) ),
      Formula( list_random( 0, 1, "d", "e" ) ) ],
    [ Formula( list_random( "d", "e" ) ),
      Formula( list_random( 0, 1 ) ),
      Formula( list_random( 0, 1 ) ) ],
    [ 0, 0, 1 ]
] );
$L4 = Matrix( [
    [ 1, 0, 0, Formula("u") ],
    [ 0, 1, 0, Formula("v") ],
    [ 0, 0, 1, Formula("w") ],
    [ 0, 0, 0, 1 ]
] );
$R4 = Matrix( [
    [ Formula("x"), 0, 0, 0 ],
    [ 0, Formula("y"), 0, 0 ],
    [ 0, 0, Formula("z"), 0 ],
    [ 0, 0, 0, 1 ]
] );
if ( random(0,1) == 1 ) {
    $tmp = $R4;
    $R4 = $L4;
    $L4 = $tmp;
}
$v1 = Formula( list_random( "u", "v", "w", "x", "y", "z" ) );
$v2 = Formula( list_random( "u", "v", "w", "x", "y", "z" ) );
$Lv = Matrix( [ [ $v1, 0, 0, $v2 ], [ 0, $v1, 0, $v2 ], [ 0, 0, $v1, $v2 ], [ 0, 0, 0, 1 ] ] );
$Rv = Matrix( [ [ random(1,9) ], [ random(1,9) ], [ random(1,9) ], [ 1 ] ] );

TEXT(beginproblem());
BEGIN_PGML
Compute the results of each matrix multiplication shown below.

[`[$L3][$R3]=`][_____]*{$L3*$R3} [@ helpLink("matrices") @]*

[`[$L4][$R4]=`][_____]*{$L4*$R4} [@ helpLink("matrices") @]*

[`[$Lv][$Rv]=`][_____]*{$Lv*$Rv} [@ helpLink("matrices") @]*
END_PGML

BEGIN_PGML_SOLUTION
[`[$L3][$R3]=[$L3*$R3]`]

[`[$L4][$R4]=[$L4*$R4]`]

[`[$Lv][$Rv]=[$Lv*$Rv]`]
END_PGML_SOLUTION

ENDDOCUMENT();