Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision Next revision | Previous revision | ||
linear_algebra:02_equations_and_matrices [2014/01/13 19:46] marje |
linear_algebra:02_equations_and_matrices [2014/01/20 12:38] marje |
||
---|---|---|---|
Line 40: | Line 40: | ||
where $\ x_1,\ x_2,\ \dots\ ,\ x_n$ are the unknowns, $\ a_{11},\ a_{12},\ \dots\ ,\ a_{mn}$ | where $\ x_1,\ x_2,\ \dots\ ,\ x_n$ are the unknowns, $\ a_{11},\ a_{12},\ \dots\ ,\ a_{mn}$ | ||
are the coefficients of the system, and $\ b_1,\ b_2,\ \dots\ ,\ b_m $ are the constant terms. | are the coefficients of the system, and $\ b_1,\ b_2,\ \dots\ ,\ b_m $ are the constant terms. | ||
- | According to [[matrices#m_multiplication|matrix multiplication]] | + | According to [[01_matrices#m_multiplication|matrix multiplication]] |
$$ | $$ | ||
Line 73: | Line 73: | ||
$$ | $$ | ||
- | we can write down the system [[equations_and_matrices#lin_system_1|$(\ast)$]] in matrix notation as follows | + | we can write down the system [[02_equations_and_matrices#lin_system_1|$(\ast)$]] in matrix notation as follows |
<columns 100% m 10% l> | <columns 100% m 10% l> | ||
Line 122: | Line 122: | ||
where the firts row represence the first equation, the second row represence the second equation and so on, | where the firts row represence the first equation, the second row represence the second equation and so on, | ||
- | has exactly the same information as the original system [[equations_and_matrices#lin_system_2|$(\ast\ast)$]]. | + | has exactly the same information as the original system [[02_equations_and_matrices#lin_system_2|$(\ast\ast)$]]. |
The augmented matrix can be used for solving the system of linear equations. | The augmented matrix can be used for solving the system of linear equations. | ||
Line 167: | Line 167: | ||
\end{array} | \end{array} | ||
\right. | \right. | ||
- | \quad\overset{R_2-2\cdot R_1}\Longleftrightarrow | + | \overset{R_2-2\cdot R_1}\Longleftrightarrow |
\left\{ | \left\{ | ||
\begin{array}{rrrrr} | \begin{array}{rrrrr} | ||
Line 174: | Line 174: | ||
\end{array} | \end{array} | ||
\right. | \right. | ||
- | \quad\overset{\frac{1}{8}\cdot R_2}\Longleftrightarrow | + | \overset{\frac{1}{8}\cdot R_2}\Longleftrightarrow |
\left\{ | \left\{ | ||
\begin{array}{rrrrr} | \begin{array}{rrrrr} | ||
Line 181: | Line 181: | ||
\end{array} | \end{array} | ||
\right. | \right. | ||
- | \quad\overset{R_1+2\cdot R_2}\Longleftrightarrow | + | \overset{R_1+2\cdot R_2}\Longleftrightarrow |
\left\{ | \left\{ | ||
\begin{array}{rrrrr} | \begin{array}{rrrrr} | ||
Line 229: | Line 229: | ||
<WRAP nl> | <WRAP nl> | ||
- | [[linear_algebra:03_gaussian_elimination|3. Gaussian elimination algorithm]] | + | [[linear_algebra:03_gaussian_elimination]] |
</WRAP> | </WRAP> |