diff --git a/hw5/hw5.pdf b/hw5/hw5.pdf
index 62d60c0..c2e9008 100644
Binary files a/hw5/hw5.pdf and b/hw5/hw5.pdf differ
diff --git a/hw5/hw5.tex b/hw5/hw5.tex
index 7d9f7b9..0de4317 100644
--- a/hw5/hw5.tex
+++ b/hw5/hw5.tex
@@ -109,4 +109,65 @@ Q = \frac9{16} + \frac14 \cdot \frac14 = \frac{10}{16}\]
 + f\left(1\right)\right) = \frac7{16} - \frac12 \cdot \frac34 = \frac1{16} < \frac1{10}\]
 
 Thus the solution using quadrature is $\frac{5}{8}$.
+
+\section*{Question 4}
+
+\[\begin{bmatrix} x_0^2 & x_0 & 1 \\x_1^2 & x_1 & 1 \\x_2^2 & x_2 & 1 \\x_3^2 &
+  x_3 & 1 \end{bmatrix} \begin{bmatrix}a \\b\\c\\\end{bmatrix} = \begin{bmatrix}
+y_0 \\y_1\\y_2\\y_3\\\end{bmatrix}\]
+
+\[\begin{bmatrix} x_0^2 & x_1^2 & x_2^2 & x_3^2 \\ x_0 & x_1 & x_2 & x_3 \\
+1&1&1&1\end{bmatrix} \begin{bmatrix} x_0^2 & x_0 & 1 \\x_1^2 & x_1 & 1 \\x_2^2 & x_2 & 1 \\x_3^2 &
+  x_3 & 1 \end{bmatrix} \begin{bmatrix}a \\b\\c\\\end{bmatrix} = \begin{bmatrix} x_0^2 & x_1^2 & x_2^2 & x_3^2 \\ x_0 & x_1 & x_2 & x_3 \\
+  1&1&1&1\end{bmatrix} \begin{bmatrix} y_0 \\y_1\\y_2\\y_3\\\end{bmatrix}\]
+
+\[\begin{bmatrix}18&8&6\\8&6&2\\6&2&4\\\end{bmatrix}\begin{bmatrix}a\\b\\c\\\end{bmatrix}=\begin{bmatrix}2\\0\\2\\\end{bmatrix}\]
+
+We now use Gaussian \textit{ellimination} to solve the system:
+
+\[
+  \begin{array}{@{}ccc|c@{}}
+  18&8&6&2\\
+  8&6&2&0\\
+  6&2&4&2\\
+  \end{array}
+  \qquad
+  \begin{array}{@{}ccc|c@{}}
+  1&\frac49	&\frac13 &	\frac19\\
+  8&	6&	2	&0\\
+  6	&2	&4	&2\\
+  \end{array}
+  \qquad
+  \begin{array}{@{}ccc|c@{}}
+    1&	\frac49&	\frac13&	\frac19\\
+    0&	\frac{22}9&	\frac{-2}3&	\frac{-8}9\\
+    0&	\frac{-2}3&	2&	\frac43\\
+  \end{array}
+  \qquad
+  \begin{array}{@{}ccc|c@{}}
+    1&	\frac49&	\frac13&	\frac19\\
+    0	&1	&\frac{-3}{11} & \frac{-4}{11}\\
+    0	& \frac{-2}{3} & 2	& \frac43\\
+  \end{array}
+\]\[
+  \begin{array}{@{}ccc|c@{}}
+    1&	0&	\frac5{11}	&\frac3{11}\\
+    0	&1	&\frac{-3}{11}&\frac{-4}{11}\\
+    0	&0	&\frac{20}{11}&\frac{12}{11}\\
+ \end{array}
+  \qquad
+  \begin{array}{@{}ccc|c@{}}
+    1&	0	&\frac5{11}	& \frac{3}{11}\\
+    0	&1	& \frac{-3}{11} &	\frac{-4}{11}\\
+    0&	0&	1	&\frac35\\
+ \end{array}
+  \qquad
+  \begin{array}{@{}ccc|c@{}}
+    1	&0	&0	&0\\
+    0&	1	&0	&\frac{-1}5\\
+    0&	0&	1	&\frac35\\
+ \end{array}
+  \qquad
+  \begin{bmatrix}a\\b\\c\\\end{bmatrix}=\begin{bmatrix}0\\-\frac15\\\frac35\\\end{bmatrix}
+\]
 \end{document}