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linear_algebra:02_equations_and_matrices [2014/01/13 19:46] marje |
linear_algebra:02_equations_and_matrices [2014/01/20 12:32] marje |
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| 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]] |
| $$ | $$ | ||
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| $$ | $$ | ||
| - | 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> | ||
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| 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. | ||
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| <WRAP nl> | <WRAP nl> | ||
| - | [[linear_algebra:03_gaussian_elimination|3. Gaussian elimination algorithm]] | + | [[linear_algebra:03_gaussian_elimination]] |
| </WRAP> | </WRAP> | ||