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\begin{center}
{\Large Review for Test 1}
\end{center}


\begin{itemize}
  \item  Test 1 is on Monday, September 23.
  \item  Test 1 will cover Chapter 1 and Sections 2.1 and a small part of 2.2.
\end{itemize}

\textbf{Main Ideas Covered}
\begin{enumerate}
\item  Vector Spaces
  \begin{itemize}
  \item  Operaions and properties (vector addition and scalar multiplication and their properties.
  \item  What are the examples we know of vector spaces?
  \item  Subspaces (what is one and what are some examples of subspaces?)
  \item  Null space
  \item  Column space
  \item  Span
  \end{itemize}

\item  Systems of equations - our main tool
  \begin{itemize}
  \item  Gaussian elimination
  \item  Echelon form and reduced row echelon form.
  \item  Writing a solution down (the book often uses the term parametric form, what does this mean?)
  \item  Translation vectors and spanning vectors (what are these in this context?)
  \end{itemize}

\item  Linear independence
  \begin{itemize}
  \item  We had two definitions of this, what are they?
  \item  How to check if a set of vectors is linearly independent or linearly dependent (solving systems!)
  \item  How to write a vector as a combination of others.
  \end{itemize}

\item  Dimension (we have not fully covered this item, but you are still repsonsible for whats below)
  \begin{itemize}
  \item  Definition of dimension
  \item  Definition of basis
  \item  Example of a basis for $\R^n$.
  \end{itemize}
  
\end{enumerate}

\textbf{What to expect:}

\begin{enumerate}

\item  Computational problems (for example can you actually perform elimination on a matrix by hand?)
\item  Set up problems (can you get a problem set up and ready to solve?).
  For example, if I ask you to see if a set of vectors is linearly independent of linearly dependent, 
  can you set up the equations to solve?
\item  Interpretation problems (can you interpret a solution?).
  For example, if I give you a reduced row echelon matrix can you read off the solution
  and the consequences of that solution.


\end{enumerate}

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