Row Operations

Row operations on a Matrix

Complete Code

PG problem file

Explanation

Context('Matrix');

do {
    $A = Matrix([
        [ non_zero_random(-5, 5), non_zero_random(-5, 5) ],
        [ non_zero_random(-5, 5), non_zero_random(-5, 5) ],
        [ non_zero_random(-5, 5), non_zero_random(-5, 5) ],
    ]);
} until (($A->row(1) != $A->row(2))
        && ($A->row(1) != $A->row(3))
        && ($A->row(2) != $A->row(3)));

$k  = random(2, 9);
$op = "R_{1} + $k R_{2} \rightarrow R_{1}";

$ans = 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.

The do/until loop ensures that no two rows are identical. This is not necessary for this problem, but can be helpful in other situations.

BEGIN_PGML
Give the result of applying the row operation [`[$op]`] to the given matrix.

[``[$A] \mathop{\longrightarrow}^{[$op]}``] [_____]*{$ans}
END_PGML

Statement

Remember to append a * to use an array answer rule in PGML.

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.