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\begin{hwsection}{4.1}{Vector Spaces}
  {1--12, 20 -- 26} {2, 4, 5,6, 8, 10, 11, 12, 20, 21,22, 24, 26}
\end{hwsection}

 
\begin{hwsection}{4.2}{Null Space and column space} 
  {1--9, 15, 16, 23, 24, 25, 26, 31, 32} {2, 4, 5, 6, 7, 8, 16, 23,
    24, 26, 32}
\end{hwsection}

\begin{hwsection}{4.3}{Linearly independent sets and bases} 
  {1,2,3,5,9,10,11,13,14,15,16,19,20,21,22,29,30}
  {2,3,10,14,16,20,19,22,30}
\end{hwsection}

\begin{hwsection}{4.4}{Coordinate systems}
  {1,3,4,6,7,8,9,10,11,12,13,14,15,16,18,19,27,28,29,30}
  {3,4,6,8,10,11,14,16,18,27,30}
\end{hwsection}

\begin{hwsection}{4.5}{Dimension of a vector space}
  {1,2,3,5,6,7,8,11,12,13,14,15,16,17,19,20,21,22,25,26,27,28--32}
  {2,5,6,8,12,14,17,20,22,26,28,29,31}
\end{hwsection}

\begin{hwsection}{4.6}{Rank}
  {1--14,17,18,19,20,27,28,29,30} {2,3,4,6,8,10,11,12,14,18,19,28,30}
\end{hwsection}

\begin{hwsection}{4.7}{Change of Basis}
  {1,2,3,4,5,6,7,8,9,10,11,12,13,14} {2,3,4,6,8,9,10,12,14}
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