# Commits

committed dae4b71

Line breaks, Archetype summaries

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# File changes.txt

 Edit:  Added multiplicities to Solution EE.C19 (Duncan Bennett)
 Edit:  Subsection IVLT.SLELT, reference Definition MVP for T's definition (Kyle Whitcomb)
 Edit:  Completed Solution ILT.C27 (Duncan Bennett)
+Edit:  About 130 line-break adjustments, for 5 inch text width at 10pt
 Change:  Replaced Definition RR by an informal discussion
 Change:  Definition TSVS renamed as Definition SSVS
 Change:  Proof Technique D: discussion about definitions as nouns, adjectives

# File src/archetypes.xml


 <shortsummary>Consistent system with $5\times 2$ coefficient matrix</shortsummary>

-<summary>System with five equations, two variables.  Consistent.  Null space of coefficient matrix has dimension 0.  Coefficient matrix identical to that of Archetype H, constant vector is different.</summary>
+<summary>System with five equations, two variables.  Consistent.  Null space of coefficient matrix has dimension 0.  Coefficient matrix identical to that of <acroref type="archetype" acro="H" />, constant vector is different.</summary>

 <systemdefn><alignmath>
 <![CDATA[2x_1  + 3x_2  &= 6 \\]]>

 <shortsummary>Invertible linear transformation, abstract vector spaces, equal dimension domain and codomain</shortsummary>

-<summary>Domain is polynomials, codomain is matrices.  Domain and codomain both have dimension 4.   Injective,  surjective,  invertible. Square matrix representation, but domain and codomain are unequal, so no eigenvalue information.</summary>
+<summary>Domain is polynomials, codomain is matrices.  Both domain and codomain have dimension 4.   Injective,  surjective,  invertible. Square matrix representation, but domain and codomain are unequal, so no eigenvalue information.</summary>

 <ltdefn>\ltdefn{T}{P_3}{M_{22}},\quad\lt{T}{a+bx+cx^2+dx^3}=
 \begin{bmatrix}

 <summary>Domain is polynomials, codomain is polynomials.  Domain and codomain both have dimension 3.  Injective, surjective, invertible, 3 distinct eigenvalues, diagonalizable.</summary>

-<ltdefn>\ltdefn{T}{P_2}{P_2},\quad
-\lt{T}{a+bx+cx^2}=
+<ltdefn><![CDATA[&\ltdefn{T}{P_2}{P_2},\\
+&\lt{T}{a+bx+cx^2}=
 \left(19a+6b-4c\right)+
-\left(-24a-7b+4c\right)+
-\left(36a+12b-9c\right)
+\left(-24a-7b+4c\right)x+
+\left(36a+12b-9c\right)x^2]]>
 </ltdefn>

 <ltnullspacebasis>\set{\ }