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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 sum of subspaces#23968
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  • Definition of system of linear equations#23416
  • Definition of the 0/trivial subspace#23814
  • Definition of the determinant in terms of the effect of elementary row operations#23726
  • Definition of the imaginary part of a vector in C^n#23790
  • Definition of the least-squares linear fit to 2-dimensional data#23951
  • Definition of the (main) diagonal of a matrix#23455
  • Definition of the real part of a vector in C^n#23789
  • Definition of the standard basis of the m by n matrices#23834
  • Definition of the standard basis of the polynomials of degree at most n#23833
  • Definition of the standard matrix for a linear transformation#23857
  • Definition of the standard/natural basis of R^n (or C^n)#23830
  • Definition of trace of a matrix#23715
  • Definition of transpose of a matrix#23503
  • Definition of trivial linear dependence relation on a set of vectors#23817
  • Definition of trivial solution to a homogeneous linear system of equations#23436
  • Definition of unitary matrix#23588
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  • Definition of unit vector#23909
  • Definition of Vandermonde matrix#23594
  • Definition of vector#23779
  • Definition of vector addition#23955
  • Definition of vector-scalar multiplication#23792
  • Definition of vector sum/addition#23786
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