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hw3: done 1,2,3,4,6

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Claudio Maggioni (maggicl) 2020-04-22 14:08:11 +02:00
parent 178843e24a
commit a99a3a210a
2 changed files with 66 additions and 79 deletions
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hw3/hw3.tex
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@ -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}