Are you using the latest release of Maple, 17? There are significant advances in Maple 17 that pertain to your question.

@bryon So far, the "Sorry, something went wrong" bug seems to be fixed for me. Thanks.

@acer I think that the Asker was expecting a plot that looks like the original distribution. The reason that their commands didn't provide it is that EmpiricalDistribution is a discrete distribution. Acer, I'm guessing that your solution is equivalent to tallying into bins of width 0.01. Was that your intention? A FrequencyPlot of the sample data also gives such a plot. Why did you send two bins adjacent to zero to NULL? Note the bold streaks along the vertical axis in Markiyan's post of your plots.

@acer I think that the Asker was expecting a plot that looks like the original distribution. The reason that their commands didn't provide it is that EmpiricalDistribution is a discrete distribution. Acer, I'm guessing that your solution is equivalent to tallying into bins of width 0.01. Was that your intention? A FrequencyPlot of the sample data also gives such a plot. Why did you send two bins adjacent to zero to NULL? Note the bold streaks along the vertical axis in Markiyan's post of your plots.

@Manny08 In that worksheet, a "dependency relation" is shown. That means that one column is expressed as a linear combination of the others. That one column is the same as the vector in the present problem which we want to express as a linear combination of the others. That worksheet is literally the complete answer to the present problem.

Here's an attempt explain it in simpler language: The entries in the last column of the RREF are the coefficients that are used with the original vectors to express the original last column as a linear combination of the other columns.

@bryon Could you be more specific as to what you mean by the "reply-to problem"? I am guessing that you don't mean the "Sorry, something went wrong" problem, because I just got that while writing an earlier copy of this reply.

Another MaplePrimes editor bug: The hyperlink editor is broken in Firefox. I tried several times to use it, but all I get is a blank window. It works in Internet Explorer. I mean the hyperlink editor in the old MaplePrimes editor, the one that is used when one clicks Edit on a post.

@Manny08 Why can't you follow the answer in the hyperlink in my first Reply to this post? It is literally the same answer as to the present Question. I could cut-and-paste and put that answer here. Why can't you? I'm not trying to be offensive; I'm really curious what's going on.

How about showing some example plots where you have done this, ones where you think that you did an especially good job?

Also, I do not get an error message when trying to plot your first example.

@Manny08 Yes, the RREF is the key to it all. So how do you input the matrix into Maple and compute the RREF? We've done this before.

This question is nearly identical to a question that you asked two weeks ago, http://www.mapleprimes.com/questions/145068-How-Do-I-Find-Out-If-A-Matrix-Is-Linearly, and that I answered. Even the vectors are the same. What have you learned from your previous questions and their answers on this list? Can you describe the steps by which you would solve this problem without Maple? I am willing to help you step by step, but I won't just give you the answer.

In other words, I believe that what you want is essentially the ability to format code comments using Maple's significant document formatting ability. Another way of looking at it: Instead of a document with embedded code regions, you'd like a long piece of code with embedded document regions. It sounds like a great idea. For years I've wanted an alternative to plaintext comments. 

@wb_jerry Your message was perfectly clear. I encountered the same problem myself, and I thought that that may have been your reason. I think that I have found a way around the problem. I will post it soon.

@wb_jerry Your message was perfectly clear. I encountered the same problem myself, and I thought that that may have been your reason. I think that I have found a way around the problem. I will post it soon.

@Markiyan Hirnyk Using additionally causes yet another copy of the variable to be made. I don't know if this is a bug or the intended behavior. If it was intended, I can't see any good reason for it. I hope the following examples provide understanding. Most interesting is that all copies end up with the same assumptions. For more understanding, procedures assume and additionally are written in Maple.

restart;
x0:= x:
assume(x>1);
x1:= x:
x1-x0;
                               0
additionally(x>2);
x2:= x;
                               x~
x1-x2;
                             x~ - x~
x0-x1;
                             x~ - x~
x0-x2;
                               0
ToInert(x0);
          _Inert_LOCALNAME("x~", 18446744073905239102)
ToInert(x1);
          _Inert_LOCALNAME("x~", 18446744073903233086)
ToInert(x2);
          _Inert_LOCALNAME("x~", 18446744073905239102)
about(x0);
Originally x, renamed x~:
  is assumed to be: RealRange(Open(2),infinity)

about(x1);
Originally x, renamed x~:
  is assumed to be: RealRange(Open(2),infinity)

about(x2);
Originally x, renamed x~:
  is assumed to be: RealRange(Open(2),infinity)