diff --git a/hw3/hw3.pdf b/hw3/hw3.pdf
index eb0d61b..7491c8c 100644
Binary files a/hw3/hw3.pdf and b/hw3/hw3.pdf differ
diff --git a/hw3/hw3.tex b/hw3/hw3.tex
index 44ea329..b83a66b 100644
--- a/hw3/hw3.tex
+++ b/hw3/hw3.tex
@@ -179,93 +179,80 @@ U =
 \]
 
 \section*{Question 4}
-A =
+\[
+A_1 = \begin{bmatrix}
 
-       1              4              8              3       
-       4             20             40             28       
-       8             40             89             71       
-       3             28             71            114       
+       1    &          4   &           8    &          3  \\     
+       4     &        20     &        40     &        28  \\
+       8      &       40      &       89      &       71  \\
+       3       &      28       &      71       &     114  \\
+\end{bmatrix}
+\]
 
+\[ i = 1 \hspace{1cm} l_1 = \begin{bmatrix}1\\4\\8\\3\\\end{bmatrix}\]
 
-ans =
+\[
+A_2 = \begin{bmatrix}
 
-       1       
-       4       
-       8       
-       3       
+       1    &          4   &           8    &          3  \\     
+       4     &        20     &        40     &        28  \\
+       8      &       40      &       89      &       71  \\
+       3       &      28       &      71       &     114  \\
+\end{bmatrix}
+-
+\begin{bmatrix}
+       1      &        4  &            8   &           3\\
+       4       &      16   &          32    &         12\\
+       8        &     32    &         64     &        24\\
+       3         &    12     &        24      &        9\\
+\end{bmatrix}
+=
+\begin{bmatrix}
+\\
+& 4 & 8 & 16\\       
+& 8 & 25 & 47 \\      
+& 16 & 47 & 105 \\
+\end{bmatrix}
+\]      
 
+\[i=2 \hspace{1cm} l_2 = \begin{bmatrix}\\2\\4\\8\\\end{bmatrix}\]
 
-S =
+\[A_3 = 
+\begin{bmatrix}
+\\
+& 4 & 8 & 16\\       
+& 8 & 25 & 47 \\      
+& 16 & 47 & 105 \\
+\end{bmatrix}
+-
+\begin{bmatrix}
+\\       
+& 4 & 8 & 16 \\       
+& 8 & 16 & 32  \\     
+& 16 & 32 & 64   \\    
+\end{bmatrix}
+=
+\begin{bmatrix}\\\\&& 9 & 15 \\&&15 & 41\\\end{bmatrix}
+\]
 
-       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       
+\[i = 3 \hspace{1cm} l_3 = \begin{bmatrix}\\\\3\\5\\\end{bmatrix}\]
+\[A_4 = 
+\begin{bmatrix}\\\\&& 9 & 15 \\&&15 & 41\\\end{bmatrix}
+-
+\begin{bmatrix}
+\\
+\\
+&&9&15\\
+&& 15 & 25\\       
+\end{bmatrix}
+=
+\begin{bmatrix}
+\\\\\\&&&16\\
+\end{bmatrix}       
+\]
 
+\[i = 4 \hspace{1cm} l_4 = \begin{bmatrix}\\\\\\4\\\end{bmatrix}\]
 
+\[L = \begin{bmatrix}1\\4&2\\8&4&3\\3&8&5&4\\\end{bmatrix}\]
 
 \end{document}