diff --git a/hw5/hw5.pdf b/hw5/hw5.pdf
index c2e9008..b7e3edd 100644
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diff --git a/hw5/hw5.tex b/hw5/hw5.tex
index 0de4317..d2ea741 100644
--- a/hw5/hw5.tex
+++ b/hw5/hw5.tex
@@ -170,4 +170,15 @@ We now use Gaussian \textit{ellimination} to solve the system:
   \qquad
   \begin{bmatrix}a\\b\\c\\\end{bmatrix}=\begin{bmatrix}0\\-\frac15\\\frac35\\\end{bmatrix}
 \]
+
+\section*{Question 5}
+\[\begin{bmatrix}1&0\\0&1\\-1&0\\0&-1\\1&0\\\end{bmatrix}\begin{bmatrix}a\\b\end{bmatrix}
+  = \begin{bmatrix}\frac32\\2\\-\frac12\\-2\\1\end{bmatrix}\]
+    \[\begin{bmatrix}1&0&-1&0&1\\0&1&0&-1&0\end{bmatrix}\begin{bmatrix}1&0\\0&1\\-1&0\\0&-1\\1&0\\\end{bmatrix}\begin{bmatrix}a\\b\end{bmatrix}
+  =
+  \begin{bmatrix}1&0&-1&0&1\\0&1&0&-1&0\end{bmatrix}\begin{bmatrix}\frac32\\2\\-\frac12\\-2\\1\end{bmatrix}\]
+    \[\begin{bmatrix}3&0\\0&2\end{bmatrix}\begin{bmatrix}a\\b\end{bmatrix} =
+      \begin{bmatrix}3\\2\end{bmatrix} \qquad \begin{bmatrix}a\\b\end{bmatrix} =
+        \begin{bmatrix}1\\1\end{bmatrix}\]
+
 \end{document}