** Using WeBWorK **

To be clear, I would like to have a symbolic matrix that matches the matrix I am computing with so as to prevent asking the students a different question in text

then the one I am asking in the answers. Below is an example and if I change the

matrix in the matrix context, $U and don't or forget to change the latex displayed matrix in the \bmatrix bit, the students will be doing what I ask in the displayed problem but will not get the correct answers if $U doesn't match.

If the two versions are side by side in the preamble that would be ok also....

DOCUMENT();

loadMacros("PG.pl",
"PGbasicmacros.pl",
"PGstandard.pl",
"PGML.pl",
"MathObjects.pl",
"PGcourse.pl",
#"PGmatrixmacros.pl",
# "parserPopUp.pl",
#"parserVectorUtils.pl",
);

TEXT(beginproblem());
$showPartialCorrectAnswers = 1;

######################################################################

#SRAND($psvn);

$seed = random(1,100);
SRAND($seed);



##################################
#
# Setup
#
#
Context("Matrix");

#Set up the SVD decomposition


$U = Matrix([[1/sqrt(2),-1/sqrt(2)],
[1/sqrt(2),1/sqrt(2)]]);


$V = Matrix([[0,1],
[1,0]]);

$S = Matrix([[Compute(random(4,6)),0],
[0,Compute(non_zero_random(1,3))]]);

$VT = $V->transpose;
$UT=$U->transpose;
$SI=$S->inverse;
$A = $U*$S*$VT;
#Randomly generate x
$x = sqrt(2)*Matrix([[Compute(non_zero_random(-2,2))],[Compute(non_zero_random(1,3))]]);

$b = $A*$x;
$z=$UT*$b;
$y=$SI*$z;



BEGIN_PGML

Use the given SVD factorization of [` A = U S V^{T} `]

[``A = \begin{bmatrix} \frac{1}{\sqrt{2}} & \frac{-1}{\sqrt{2}} \\
\frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \end{bmatrix} [$S] [$V]^{T}``]

Solve [` A x = [$b] `] by completing the three steps outlined in the text:

Step 1: Letting [` z = S V^{T} x`], [` A x = b `] is the same as
[` U z = [$b]`]. Since [` U `] is orthogonal, it follows that
[`` z = U^{T} b ``] = [___]*{$z}

Step 2: We now have [` S V^{T} x = U^{T} b = z`] so letting
[` y = V^{T} x `], we have [` S y = U^{T}b = z `], it follows that
[`` y = S^{-1} z ``] = [___]*{$y}

Step 3: And finally since [` V^{T} x = y `], we see that
[``x = V y ``] = [___]*{$x}.

END_PGML

ENDDOCUMENT();

This works for me in WW 2.14. But I had to use a Formula MathObject, not a Matrix. Depending on what else you are doing with $U, that may not be good.

EDIT: Now I see your more recent post. You are using things like the transpose method, which I will assume do not work on a Formula. But you could get around this by doing like:

$UforDisplay = Formula(...);

$U = Matrix("$UforDisplay");

and use them separately.

DOCUMENT();

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

Context("Matrix")->flags->set(reduceConstants=>0,reduceConstantFunctions=>0);

$U = Formula("[
[sqrt(2),sqrt(2)],
[-sqrt(2),sqrt(2)]
]");

BEGIN_PGML
[`[$U]`]
END_PGML

ENDDOCUMENT();