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rbeezer  committed 9dc9c70

LaTeX rules for fill-in-the-blank exercises (Julie Nelson)

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 Typo:  Section LT, after Example MFLT, "not an accident" (Kyle Whitcomb)
 Typo:  Section SLT, before Diagram SLT, domain/codomain confusion (Kyle Whitcomb)
 Typo:  Section IVLT, after Definition IVS, "given", "a" reversed (Kyle Whitcomb)
+Typo:  LaTeX rules for fill-in-the-blank exercises (Julie Nelson)
 
 MAJOR SOURCE FORMAT CHANGE
 ~~~~~~~~~~~~~~~~~~~~~~~~~~

File src/section-ILT.xml

 </exercise>
 
 <exercise type="M" number="60" rough="zero linear transformation">
-<problem contributor="robertbeezer">Suppose $U$ and $V$ are vector spaces.  Define the function $\ltdefn{Z}{U}{V}$ by $\lt{T}{\vect{u}}=\zerovector_{V}$ for every $\vect{u}\in U$.  Then by <acroref type="exercise" acro="LT.M60" />, $Z$ is a linear transformation.  Formulate a condition on $U$ that is equivalent to $Z$ being an injective linear transformation.   In other words, fill in the blank to complete the following statement (and then give a proof):  $Z$ is injective if and only if $U$ is \rule{1in}{1pt}. (See <acroref type="exercise" acro="SLT.M60" />, <acroref type="exercise" acro="IVLT.M60" />.)
+<problem contributor="robertbeezer">Suppose $U$ and $V$ are vector spaces.  Define the function $\ltdefn{Z}{U}{V}$ by $\lt{T}{\vect{u}}=\zerovector_{V}$ for every $\vect{u}\in U$.  Then by <acroref type="exercise" acro="LT.M60" />, $Z$ is a linear transformation.  Formulate a condition on $U$ that is equivalent to $Z$ being an injective linear transformation.   In other words, fill in the blank to complete the following statement (and then give a proof):  $Z$ is injective if and only if $U$ is  <rule width="1in" height="1pt" />. (See <acroref type="exercise" acro="SLT.M60" />, <acroref type="exercise" acro="IVLT.M60" />.)
 </problem>
 </exercise>
 

File src/section-IVLT.xml

 </exercise>
 
 <exercise type="M" number="60" rough="zero linear transformation">
-<problem contributor="robertbeezer">Suppose $U$ and $V$ are vector spaces.  Define the function $\ltdefn{Z}{U}{V}$ by $\lt{T}{\vect{u}}=\zerovector_{V}$ for every $\vect{u}\in U$.  Then by <acroref type="exercise" acro="LT.M60" />, $Z$ is a linear transformation.  Formulate a condition on $U$ and $V$ that is equivalent to $Z$ being an invertible linear transformation.   In other words, fill in the blank to complete the following statement (and then give a proof):  $Z$ is invertible if and only if $U$ and $V$ are \rule{1in}{1pt}. (See <acroref type="exercise" acro="ILT.M60" />, <acroref type="exercise" acro="SLT.M60" />, <acroref type="exercise" acro="MR.M60" />.)
+<problem contributor="robertbeezer">Suppose $U$ and $V$ are vector spaces.  Define the function $\ltdefn{Z}{U}{V}$ by $\lt{T}{\vect{u}}=\zerovector_{V}$ for every $\vect{u}\in U$.  Then by <acroref type="exercise" acro="LT.M60" />, $Z$ is a linear transformation.  Formulate a condition on $U$ and $V$ that is equivalent to $Z$ being an invertible linear transformation.   In other words, fill in the blank to complete the following statement (and then give a proof):  $Z$ is invertible if and only if $U$ and $V$ are  <rule width="1in" height="1pt" />. (See <acroref type="exercise" acro="ILT.M60" />, <acroref type="exercise" acro="SLT.M60" />, <acroref type="exercise" acro="MR.M60" />.)
 </problem>
 </exercise>
 

File src/section-SLT.xml

 </exercise>
 
 <exercise type="M" number="60" rough="zero linear transformation">
-<problem contributor="robertbeezer">Suppose $U$ and $V$ are vector spaces.  Define the function $\ltdefn{Z}{U}{V}$ by $\lt{T}{\vect{u}}=\zerovector_{V}$ for every $\vect{u}\in U$.  Then by <acroref type="exercise" acro="LT.M60" />, $Z$ is a linear transformation.  Formulate a condition on $V$ that is equivalent to $Z$ being an surjective linear transformation.   In other words, fill in the blank to complete the following statement (and then give a proof):  $Z$ is surjective if and only if $V$ is \rule{1in}{1pt}. (See <acroref type="exercise" acro="ILT.M60" />, <acroref type="exercise" acro="IVLT.M60" />.)
+<problem contributor="robertbeezer">Suppose $U$ and $V$ are vector spaces.  Define the function $\ltdefn{Z}{U}{V}$ by $\lt{T}{\vect{u}}=\zerovector_{V}$ for every $\vect{u}\in U$.  Then by <acroref type="exercise" acro="LT.M60" />, $Z$ is a linear transformation.  Formulate a condition on $V$ that is equivalent to $Z$ being an surjective linear transformation.   In other words, fill in the blank to complete the following statement (and then give a proof):  $Z$ is surjective if and only if $V$ is <rule width="1in" height="1pt" />. (See <acroref type="exercise" acro="ILT.M60" />, <acroref type="exercise" acro="IVLT.M60" />.)
 </problem>
 </exercise>