LinearSolve[m, b]
finds an x that solves the matrix equation .

generates a LinearSolveFunction[...] that can be applied repeatedly to different b.

Details and OptionsDetails and Options

  • LinearSolve works on both numerical and symbolic matrices, as well as SparseArray objects.
  • The argument b can be either a vector or a matrix. »
  • The matrix m can be square or rectangular. »
  • LinearSolve[m] and LinearSolveFunction[...] provide an efficient way to solve the same approximate numerical linear system many times.
  • LinearSolve[m, b] is equivalent to LinearSolve[m][b].
  • For underdetermined systems, LinearSolve will return one of the possible solutions; Solve will return a general solution. »
  • LinearSolve[m, b, Modulus->n] takes the matrix equation to be modulo n. »
  • LinearSolve[m, b, ZeroTest->test] evaluates to determine whether matrix elements are zero. The default setting is ZeroTest->Automatic.
  • A Method option can also be given. Settings for exact and symbolic matrices include , , and . Settings for approximate numerical matrices include , and for sparse arrays and . The default setting of Automatic switches among these methods depending on the matrix given.
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