RowOperations1

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Row Operations

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This PG code shows how to ask students to compute the result of elementary row operations.


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PG problem file Explanation

Problem tagging data

Problem tagging:

DOCUMENT();
loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"PGcourse.pl",
);
$showPartialCorrectAnswers = 0;
TEXT(beginproblem()); 

Initialization:

Context('Matrix');

do {

$A = Matrix([
[non_zero_random(-5,5,1),non_zero_random(-5,5,1)],
[non_zero_random(-5,5,1),non_zero_random(-5,5,1)],
[non_zero_random(-5,5,1),non_zero_random(-5,5,1)],
]);

} until (($A->row(1) != $A->row(2)) && 
         ($A->row(1) != $A->row(3)) && 
         ($A->row(2) != $A->row(3)));

$k = random(2,9,1);

$op = "R_{1} + $k R_{2} \rightarrow R_{1}";

$answer = Matrix([
  $A->row(1) + $k*($A->row(2)),
  $A->row(2),
  $A->row(3),
  ]);

Setup: Construct a matrix with three distinct rows. Create a string $op of Tex code that describes the row operation. Use $A->row(i) to extract the ith row of the matrix A as a MathObject. Use $A->row(1) + $k*($A->row(2)) to perform the row operation and place it into the first row of the answer matrix.

Context()->texStrings;
BEGIN_TEXT
Give the result of applying the row operation \( $op \) to the given matrix.
$BR
$BR
\( $A {\displaystyle\mathop{\longrightarrow}^{$op}} \)
\{ $answer->ans_array \}
END_TEXT
Context()->normalStrings;

Main Text:


ANS( $answer->cmp() );

COMMENT('MathObject version.');

ENDDOCUMENT();

Answer Evaluation:

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