Question 186735
1. Is it in rref?
<pre><font size = 4 color = "indigo"><b>
Yes because: going left to right, the VERY FIRST non-zero element 
in each row which isn't all zeros has these properties:

A. It is a 1.

B. It has no elements directly above it or below it other than zeros. 

C. It is farther to the right than any first non-zero element which 
   may be above it.

D. If any row has only zeros then it is at the bottom.
</pre></font></b>

2. If it is in rref, what is the solution set?
<pre><font size = 4 color = "indigo"><b>
There is no solution because, as you have discovered,
the bottom row translates to the following equation, 
where the 5th variable is {{{x[5]}}} 

     {{{0*x[5]=1}}}

which has no solution, since no matter what value you
substitute for {{{x[5]}}} the left side will always be
0 and the right side is 1, and zero can never equal 1.
So the solution set is the empty set which is either
written {{{phi}}} or {{{matrix(1,2, "{","}")}}}
</pre></font></b>
3. If it is not in rref, why?
<pre><font size = 4 color = "indigo"><b>

But it is in <font color = "red">rref</font>, which means <font color = "red">r</font>ow <font color = "red">r</font>educed <font color = "red">e</font>chelon <font color = "red">f</font>orm!

Edwin</pre>