Defactoring algorithms: Difference between revisions
ArrowHead294 (talk | contribs) m →Hermite decomposition by hand: Arrays with {c} are much better at representing augmented matrices |
ArrowHead294 (talk | contribs) m →Inversion by hand: Change to array format |
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<math> | <math> | ||
\left[ \begin{array} { | \left[ \begin{array} {ccc|ccc} | ||
3 & -2 & 4 | 3 & -2 & 4 & 1 & 0 & 0 \\ | ||
1 & 0 & | 1 & 0 & 2 & 0 & 1 & 0 \\ | ||
0 & 1 & 0 & 0 & 0 & 1 \\ | |||
\end{array} \right] | |||
1 | |||
0 & 1 & 0 | |||
0 & 0 & 1 \\ | |||
</math> | </math> | ||
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<math> | <math> | ||
\left[ \begin{array} { | \left[ \begin{array} {ccc|ccc} | ||
1 & 0 & 2 | 1 & 0 & 2 & 0 & 1 & 0 \\ | ||
0 & 1 & 0 \\ | 0 & 1 & 0 & 0 & 0 & 1 \\ | ||
3 & -2 & 4 & 1 & 0 & 0 \\ | |||
\end{array} \right] | |||
0 & 1 | |||
1 & 0 & 0 \\ | |||
</math> | </math> | ||
Okay, now let's target the bottom-right entry. How can we make that 3 into a 0? Let's subtract the 1st row from the 3rd row 3 times: | Okay, now let's target the bottom-right entry. How can we make that 3 into a 0? Let's subtract the 1st row from the 3rd row 3 times: | ||
<math>\left[ \begin{array} { | <math>\left[ \begin{array} {ccc|ccc} | ||
\color{blue}1 & \color{blue}0 & \color{blue}2 | \color{blue}1 & \color{blue}0 & \color{blue}2 & \color{blue}0 & \color{blue}1 & \color{blue}0 \\ | ||
0 & 1 & 0 & 0 & 0 & 1 \\ | |||
\color{ | \color{red}0 & \color{red}-2 & \color{red}-2 & \color{red}1 & \color{red}-3 & \color{red}0 \\ | ||
\end{array} \right] | |||
\color{ | |||
\color{red}1 & \color{red}-3 & \color{red}0 \\ | |||
</math> | </math> | ||
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<math> | <math> | ||
\left[ \begin{array} {l} \begin{matrix} | \left[ \begin{array} {l} \begin{matrix} | ||
1 & 0 & 2 \\ | 1 & 0 & 2 & 0 & 1 & 0 \\ | ||
\color{blue}0 & \color{blue}1 & \color{blue}0 | \color{blue}0 & \color{blue}1 & \color{blue}0 & \color{blue}0 & \color{blue}0 & \color{blue}1 \\ | ||
\color{ | \color{red}0 & \color{red}0 & \color{red}-2 & \color{red}1 & \color{red}-3 & \color{red}2 \\ | ||
\end{array} \right] | |||
\color{ | |||
\color{red}1 & \color{red}-3 & \color{red}2 \\ | |||
</math> | </math> | ||
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<math> | <math> | ||
\left[ \begin{array} {l} \begin{matrix} | \left[ \begin{array} {l} \begin{matrix} | ||
\color{red}1 & \color{red}0 & \color{red}0 | \color{red}1 & \color{red}0 & \color{red}0 & \color{red}1 & \color{red}-2 & \color{red}2 \\ | ||
0 & 1 & 0 & 0 & 0 & 1 \\ | |||
\color{ | \color{blue}0 & \color{blue}0 & \color{blue}-2 & \color{blue}1 & \color{blue}-3 & \color{blue}2 \\ | ||
\end{array} \right] | |||
\color{ | |||
\color{blue}1 & \color{blue}-3 & \color{blue}2 \\ | |||
</math> | </math> | ||
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<math> | <math> | ||
\left[ \begin{array} {l} \begin{matrix} | \left[ \begin{array} {l} \begin{matrix} | ||
1 & 0 & 0 \\ | 1 & 0 & 0 & 1 & -2 & 2 \\ | ||
0 & 1 & 0 \\ | 0 & 1 & 0 & 0 & 0 & 1 \\ | ||
\color{red}0 & \color{red}0 & \color{red}1 | \color{red}0 & \color{red}0 & \color{red}1 & \color{red}-\frac12 & \color{red}\frac32 & \color{red}-1 \\ | ||
\end{array} \right] | |||
\color{red}-\frac12 & \color{red}\frac32 & \color{red}-1 \\ | |||
</math> | </math> | ||