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  • 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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  1. The solutions to a nonhomogeneous system are given by a particular solution plus the solutions to the homogeneous system.

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276–300 of 715 nodes
  • Definition of row equivalent matrices#23479
  • Definition of row operations on a matrix#23475
  • Definition of row reduce a matrix#23545
  • Definition of row space of a matrix#23880
  • Definition of scalar#23778
  • Definition of scalar multiple of a linear transformation#24017
  • Definition of Schur triangulation#23633
  • Definition of similarity transform#23637
  • Definition of similar matrices#23635
  • Definition of singular matrix (not nonsingular)#23643
  • Definition of singular value decomposition (SVD)#23623
  • Definition of size of a matrix#23451
  • Definition of size of a vector#23782
  • Definition of skew-symmetric matrix#23579
  • Definition of solution set of a system of linear equations#23418
  • Definition of solution to a linear equation#23415
  • Definition of solution to a system of linear equations#23417
  • Definition of solution vector of a linear system#23758
  • Definition of spanning/generating set for a space or subspace#23978
  • Definition of span of a set of vectors#23805
  • Definition of square matrix#23454
  • Definition of subspace#23812
  • Definition of subspace spanned by a set of a set of vectors#23813
  • Definition of sum of linear transformations#24015
  • Definition of sum of matrices#23462
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