Linear systems of equations
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- Basic terminology
- Parametric form of the solution set of a system of linear equations
- Parametric vector form of the solution set of a system of linear equations
- Gaussian elimination as a method to solve a linear system
- Definition of echelon form of a linear system
- All echelon forms of a linear system have the same free variables
- Definition of equation operations on a linear system
- Equation operations on a linear system give an equivalent system.
- Definition of equivalent systems of linear equations
- The geometry of linear systems
- Definition of consistent linear system
- Definition of inconsistent linear system
- Definition of homogeneous linear system of equations
- Homogeneous linear systems are consistent.
- Definition of nontrivial solution to a homogeneous linear system of equations
- Definition of trivial solution to a homogeneous linear system of equations
- A homogeneous system has a nontrivial solution if and only if it has a free variable.
- The number of solutions to a linear system
- Definition of basic/dependent/leading variable in a linear system
- Definition of free/independent variable in a linear system
- Theorem describing the vector form of sulutions to a linear system.
- The solutions to a nonhomogeneous system are given by a particular solution plus the solutions to the homogeneous system.
- Definition of ill-conditioned linear system
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