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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 whether there is one or infinitely many solutions.

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  • Definition of codomain of a linear transformation#23841
  • Definition of coefficient matrix of a linear system#23756
  • Definition of coefficients of a linear equation#23414
  • Definition of cofactor/submatrix of a matrix#23717
  • Definition of column rank of a matrix#23673
  • Definition of column space of a matrix#23875
  • Definition of column vector#23780
  • Definition of complement of a subspace#23975
  • Definition of composition of linear transformations#24023
  • Definition of conjugate of a matrix#23465
  • Definition of conjugate of a vector in C^n#23788
  • Definition of consistent linear system#23431
  • Definition of constant vector of a linear system#23757
  • Definition of coordinates relative to a given basis#23835
  • Definition of coordinate vector/mapping/representation relative to a given basis#23991
  • Definition of cross product#24121
  • Definition of determinant of a matrix as a cofactor expansion across the first row#23718
  • Definition of determinant of a matrix as a product of the diagonal entries in a non-scaled echelon form.#23724
  • Definition of diagonalizable linear transformation#24041
  • Definition of diagonalizable matrix#23611
  • Definition of diagonal matrix#23456
  • Definition of dimension of a vector space (or subspace)#23837
  • Definition of dimension of a vector space (or subspace) being finite or infinite#24009
  • Definition of direct sum of subspaces#23970
  • Definition of distance#23911
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