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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}