# HG changeset patch
# User Santosh G. Vattam <vattam.santosh@gmail.com>
# Date 1256723275 -19800
# Node ID 68cb4265173a79ebf45b8e9899a5bcbb7b7d53e7
# Parent  c435d5846ef59d1d33be5f145affd823a3118a9c# Parent  15306dad3b8116f00ac9977feee711a996ecb403
Merged branches.

diff -r 15306dad3b81 -r 68cb4265173a day1/session4.tex
--- a/day1/session4.tex	Wed Oct 28 15:17:39 2009 +0530
+++ b/day1/session4.tex	Wed Oct 28 15:17:55 2009 +0530
@@ -282,8 +282,6 @@
     In []: b = matrix([[1], [-2], [0]])
     In []: x = linalg.solve(A, b)
     In []: Ax = dot(A, x)
-    In []: allclose(Ax, b)
-    Out[]: True
   \end{lstlisting}
 \end{frame}
 
@@ -295,13 +293,37 @@
 array([[ 1.],
        [-2.],
        [-2.]])
+\end{lstlisting}
+\end{frame}
 
+\begin{frame}[fragile]
+\frametitle{Let's check!}
+\begin{lstlisting}
 In []: Ax
 Out[]: 
 matrix([[  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}
+\end{frame}
+
+\subsection{Exercises}
+\begin{frame}[fragile]
+\frametitle{Problem 1}
+\begin{align*}
+  x + y + 2z -w & = 3\\
+  2x + 5y - z - 9w & = -3\\
+  2x + y -z + 3w & = -11 \\
+  x - 3y + 2z + 7w & = -5\\
+\end{align*}
 \end{frame}
 
 \section{Summary}