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  • Linear systems and echelon matrices

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  • The echelon form can be used to determine if a linear system is consistent.
  • Example of using the echelon form to determine if a linear system is consistent.
  • The number of pivots in the reduced row echelon form of a consistent system determines whether there is one or infinitely many solutions.
  • The number of pivots in the reduced row echelon form of a consistent system determines the number of free variables in the solution set.
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  1. The number of pivots in the reduced row echelon form of a consistent system determines the number of free variables in the solution set.

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  • Definition of distance between vectors#24091
  • Definition of domain of a linear transformation#23840
  • Definition of echelon form of a linear system#23422
  • Definition of (echelon matrix/matrix in (row) echelon form)#23539
  • Definition of eigenspace of a linear transformation#24050
  • Definition of eigenspace of a matrix#23684
  • Definition of eigenvalue/characteristic value of a linear transformation#24042
  • Definition of eigenvalue of a matrix#23681
  • Definition of eigenvector/characteristic vector of a linear transformation#24043
  • Definition of eigenvector of a matrix#23682
  • Definition of elementary matrix#23557
  • Definition of entry/component of a vector#23783
  • Definition of equality of matrices#23459
  • Definition of equality of vectors#23785
  • Definition of equation operations on a linear system#23424
  • Definition of equivalent matrices#23604
  • Definition of equivalent systems of linear equations#23426
  • Definition of extended reduced row echelon form of a matrix#23550
  • Definition of free/independent variable in a linear system#23443
  • Definition of generalized inverse of a matrix#23534
  • Definition of generalized kernel/null space of linear transformation#24060
  • Definition of generalized range space of a linear transformation#24039
  • Definition of geometric multiplicity of an eigenvalue#23697
  • Definition of Gram-Schmidt process#24093
  • Definition of Hermitian/self-adjoint matrix#23597
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