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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 Hessenberg form#23619
  • Definition of homogeneous linear system of equations#23433
  • Definition of how the action of a linear transformation on a basis extends to the whole space#23867
  • Definition of identity linear transformation#24014
  • Definition of identity matrix#23457
  • Definition of ill-conditioned linear system#23446
  • Definition of image (of a point) under a linear transformation#23842
  • Definition of inconsistent linear system#23432
  • Definition of independent subspaces#23972
  • Definition of index of nilpotency#23584
  • Definition of inner/dot product on C^n#23896
  • Definition of inner/dot product on R^n#23895
  • Definition of inner product#24088
  • Definition of inner product space#24089
  • Definition of intersection of subspaces#23966
  • Definition of invariant subspace of a linear transformation.#24052
  • Definition of inverse of a linear transformation#23849
  • Definition of inverse of a matrix#23517
  • Definition of invertible linear transformation#23848
  • Definition of invertible matrix#23518
  • Definition of invertible/nonsingular linear transformation#24021
  • Definition of isomorphic/isomorphism between vector spaces#24001
  • Definition of Jordan form#23620
  • Definition of kernel/null space of linear transformation#24058
  • Definition of kernel of linear transformation#23847
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