BUILT-IN MATHEMATICA SYMBOL

# LinearSolve

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

LinearSolve[m]
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 .
• 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.

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

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With no right-hand side, a LinearSolveFunction is returned:

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