## WeBWorK Problems

### How to in Matrix context leave un evaluated expressions

by Jack Dockery -
Number of replies: 4
How do you leave the sqrt(2) in a matrix for the text part of a question:

$U = Matrix([[1/sqrt(2),-1/sqrt(2)], [1/sqrt(2),1/sqrt(2)]]); I want the students to see \begin{bmatrix} \frac{1}{\sqrt{2} ... \end{bmatrix} when I ask the question. I am not sure how to leave these squareroots as displayed. I know this must be simple but I can't seem to find the answer anywhere. In reply to Jack Dockery ### Re: How to in Matrix context leave un evaluated expressions by Danny Glin - Have you tried$U = Matrix([["1/sqrt(2)","-1/sqrt(2)"],
["1/sqrt(2)","1/sqrt(2)"]]);

Without the quotes, you are building a Matrix object based on perl reals. With the quotes, MathObjects will parse the strings, and hopefully maintain the structure.

### Re: How to in Matrix context leave un evaluated expressions

by Jack Dockery -
I tied it but no luck ....

### How to in Matrix context leave un evaluated expressions

by Jack Dockery -
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();

"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();

### Re: How to in Matrix context leave un evaluated expressions

by Alex Jordan -
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();

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