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Wording in Exercise MM.T52 (Dan Drake)

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 Edit: Extended slightly the conclusion of Theorem HSC
 Edit: Sage CNIP, removed obsolete discussion (Michael DuBois)
 Edit: Stronger finish to proof of Theorem TT (Anna Dovzhik)
+Edit: Wording in Exercise MM.T52 (Dan Drake)
 Change: Theorem ISRN demoted to Exercise TSS.T11
 Change: Prefer "pivot columns" over "leading 1", Chapter SLE
 Typo: C^n in statement of Theorem SLSLC
 Typo: Solution LDS.T55, B should be C at very end (Chris Spalding)
 Typo: LaTeX/XML formatting in Solution LDS.T40 (Vladimir Yelkhimov)
 Typo: Property ZM of Theorem VSPM, matrix, not vector (Michael DuBois)
-Typo: LaTeX/XML formatting in Exercise MO.C10 (Anna Dovzhik)
+Typo: LaTeX/XML formatting in Exercise MO.C10 (Anna Dovzhik, Dan Drake)
 Typo: LaTeX/XML formatting in Theorem HMIP (Anna Dovzhik)
 Typo: LaTeX/XML formatting in Theorem TTMI (Gavin Tranter)
 Typo: Sage MISLE, "fuill" to "full" (Gavin Tranter)

File src/section-MM.xml

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 </exercise>
 
 <exercise type="T" number="52" rough="x,y,x+y all solutions -> homogeneous">
-<problem contributor="robertbeezer">Suppose that $\vect{x},\,\vect{y}\in\complex{n}$, $\vect{b}\in\complex{m}$ and $A$ is an $m\times n$ matrix.  If $\vect{x}$, $\vect{y}$ and $\vect{x}+\vect{y}$ are each a solution to the linear system $\linearsystem{A}{\vect{b}}$, what interesting can you say about $\vect{b}$?  Form an implication with the existence of the three solutions as the hypothesis and an interesting statement about $\linearsystem{A}{\vect{b}}$ as the conclusion, and then give a proof.
+<problem contributor="robertbeezer">Suppose that $\vect{x},\,\vect{y}\in\complex{n}$, $\vect{b}\in\complex{m}$ and $A$ is an $m\times n$ matrix.  If $\vect{x}$, $\vect{y}$ and $\vect{x}+\vect{y}$ are each a solution to the linear system $\linearsystem{A}{\vect{b}}$, what can you say that is interesting about $\vect{b}$?  Form an implication with the existence of the three solutions as the hypothesis and an interesting statement about $\linearsystem{A}{\vect{b}}$ as the conclusion, and then give a proof.
 </problem>
 <solution contributor="robertbeezer">$\linearsystem{A}{\vect{b}}$ must be homogeneous.  To see this consider that
 <alignmath>