diff --git a/hw3/hw3.pdf b/hw3/hw3.pdf
index 3782fdf..eb0d61b 100644
Binary files a/hw3/hw3.pdf and b/hw3/hw3.pdf differ
diff --git a/hw3/hw3.tex b/hw3/hw3.tex
index 99f34db..44ea329 100644
--- a/hw3/hw3.tex
+++ b/hw3/hw3.tex
@@ -178,5 +178,94 @@ U =
 \end{bmatrix}
 \]
 
+\section*{Question 4}
+A =
+
+       1              4              8              3       
+       4             20             40             28       
+       8             40             89             71       
+       3             28             71            114       
+
+
+ans =
+
+       1       
+       4       
+       8       
+       3       
+
+
+S =
+
+       1              4              8              3       
+       4             16             32             12       
+       8             32             64             24       
+       3             12             24              9       
+
+
+A =
+
+       0              0              0              0       
+       0              4              8             16       
+       0              8             25             47       
+       0             16             47            105       
+
+
+ans =
+
+       0       
+       2       
+       4       
+       8       
+
+
+S =
+
+       0              0              0              0       
+       0              4              8             16       
+       0              8             16             32       
+       0             16             32             64       
+
+
+A =
+
+       0              0              0              0       
+       0              0              0              0       
+       0              0              9             15       
+       0              0             15             41       
+
+
+ans =
+
+       0       
+       0       
+       3       
+       5       
+
+
+S =
+
+       0              0              0              0       
+       0              0              0              0       
+       0              0              9             15       
+       0              0             15             25       
+
+
+A =
+
+       0              0              0              0       
+       0              0              0              0       
+       0              0              0              0       
+       0              0              0             16       
+
+
+ans =
+
+       0       
+       0       
+       0       
+       4       
+
+
 
 \end{document}