--- a/day1/session4.tex	Thu Nov 05 13:09:17 2009 +0530
+++ b/day1/session4.tex	Thu Nov 05 13:13:58 2009 +0530
@@ -476,160 +476,6 @@
 \end{lstlisting}
 \end{frame}
 
-\section{Solving linear equations}
-
-\begin{frame}[fragile]
-\frametitle{Solution of equations}
-Consider,
-  \begin{align*}
-    3x + 2y - z  & = 1 \\
-    2x - 2y + 4z  & = -2 \\
-    -x + \frac{1}{2}y -z & = 0
-  \end{align*}
-Solution:
-  \begin{align*}
-    x & = 1 \\
-    y & = -2 \\
-    z & = -2
-  \end{align*}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Solving using Matrices}
-Let us now look at how to solve this using \kwrd{matrices}
-  \begin{lstlisting}
-    In []: A = array([[3,2,-1],
-                      [2,-2,4],                   
-                      [-1, 0.5, -1]])
-    In []: b = array([[1], [-2], [0]])
-    In []: x = solve(A, b)
-    In []: Ax = dot(A,x)
-  \end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Solution:}
-\begin{lstlisting}
-In []: x
-Out[]: 
-array([[ 1.],
-       [-2.],
-       [-2.]])
-\end{lstlisting}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Let's check!}
-\begin{lstlisting}
-In []: Ax
-Out[]: 
-array([[  1.00000000e+00],
-       [ -2.00000000e+00],
-       [  2.22044605e-16]])
-\end{lstlisting}
-\begin{block}{}
-The last term in the matrix is actually \alert{0}!\\
-We can use \kwrd{allclose()} to check.
-\end{block}
-\begin{lstlisting}
-In []: allclose(Ax, b)
-Out[]: True
-\end{lstlisting}
-\inctime{15}
-\end{frame}
-
-\subsection{Exercises}
-
-\begin{frame}[fragile]
-\frametitle{Problem 1}
-Given the matrix:\\
-\begin{center}
-$\begin{bmatrix}
--2 & 2 & 3\\
- 2 & 1 & 6\\
--1 &-2 & 0\\
-\end{bmatrix}$
-\end{center}
-Find:
-\begin{itemize}
-  \item[i] Transpose
-  \item[ii]Inverse
-  \item[iii]Determinant
-  \item[iv] Eigenvalues and Eigen vectors
-  \item[v] Singular Value decomposition
-\end{itemize}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Problem 2}
-Given 
-\begin{center}
-A = 
-$\begin{bmatrix}
--3 & 1 & 5 \\
-1 & 0 & -2 \\
-5 & -2 & 4 \\
-\end{bmatrix}$
-, B = 
-$\begin{bmatrix}
-0 & 9 & -12 \\
--9 & 0 & 20 \\
-12 & -20 & 0 \\
-\end{bmatrix}$
-\end{center}
-Find:
-\begin{itemize}
-  \item[i] Sum of A and B
-  \item[ii]Elementwise Product of A and B
-  \item[iii] Matrix product of A and B
-\end{itemize}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Solution}
-Sum: 
-$\begin{bmatrix}
--3 & 10 & 7 \\
--8 & 0 & 18 \\
-17 & -22 & 4 \\
-\end{bmatrix}$
-,\\ Elementwise Product:
-$\begin{bmatrix}
-0 & 9 & -60 \\
--9 & 0 & -40 \\
-60 & 40 & 0 \\
-\end{bmatrix}$
-,\\ Matrix product:
-$\begin{bmatrix}
-51 & -127 & 56 \\
--24 & 49 & -12 \\
-66 & -35 & -100 \\
-\end{bmatrix}$
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Problem 3}
-Solve the set of equations:
-\begin{align*}
-  x + y + 2z -w & = 3\\
-  2x + 5y - z - 9w & = -3\\
-  2x + y -z + 3w & = -11 \\
-  x - 3y + 2z + 7w & = -5\\
-\end{align*}
-\inctime{10}
-\end{frame}
-
-\begin{frame}[fragile]
-\frametitle{Solution}
-Use \kwrd{solve()}
-\begin{align*}
-  x & = -5\\
-  y & = 2\\
-  z & = 3\\
-  w & = 0\\
-\end{align*}
-\end{frame}
-
 \section{Summary}
 \begin{frame}
   \frametitle{What did we learn??}