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Summary Of: System of linear equations

a system of linear equations may behave differently than expected if the equations are... The simplest method for solving a system of linear equations is to repeatedly eliminate variables... The standard algorithm for solving a system of linear equations is based on Gaussian elimination with some modifications...

Encyclodia Page On: System of linear equations

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A linear system in three variables determines a collection of planes. The intersection point is the solution. | | planes | mathematics | linear equations | variables | linear algebra | algorithms | numerical linear algebra | engineering | physics | chemistry | computer science | economics | approximated | linearization | mathematical model | computer simulation | elementary algebra | real | complex numbers | integers | rational numbers | algebraic structure | column vector | linear combination | vector spaces | modules | span | basis | linearly independent | dimension | matrix | column vector | rank | The solution set for the equations x – y = –1 and 3x + y = 9 is the single point (2, 3). | | set | solution set | line | intersection | empty set | plane | three-dimensional space | hyperplane | n-dimensional space | flat | The solution set for two equations in three variables is usually a line. | | dimension | | | | linearly dependent | The equations 3x + 2y = 6 and 3x + 2y = 12 are inconsistent. | | contradiction | parallel | linear independence | The equations x – 2y = –1, 3x + 5y = 8, and 4x + 3y = 7 are not linearly independent. | | algorithms | solving | degree of freedom | dimension | Gaussian elimination | augmented matrix | elementary row operations | reduced row echelon form | scalar | Gaussian elimination | Gauss-Jordan elimination | Cramer's rule | determinants | LU decomposition | symmetric | positive definite | Cholesky decomposition | Levinson recursion | Toeplitz matrices | sparse matrices | iterative methods | zero vector | vectors | scalar | linear subspace | null space | translation | flat | linear subspace | image | linear transformation | LAPACK | Row reduction | Simultaneous equations | Arrangement of hyperplanes | Linear least squares | List of linear algebra references | ISBN 978-0321287137 | ISBN 978-0898714548 | ISBN 978-0030105678 | Categories | Algebra | Equations | Linear algebra |
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