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Mathematica Teacher's Edition

Built-in Functions

Lists and Matrices

Matrix Operations

LinearSolve

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

LinearSolve works on both numerical and symbolic matrices.
The argument b can be either a vector or a matrix.
The matrix m can be square or rectangular.
For underdetermined systems, LinearSolve will return one of the possible solutions; Solve will return a general solution.
For sparse systems of linear equations, it will usually be much more efficient to use Solve than LinearSolve.
LinearSolve[m, b, Modulus -> n] takes the matrix equation to be modulo n.
See The Mathematica Book on the web: Section 3.7.8.
Implementation Notes: see Sections A.9.4 and A.9.4.
See also: Inverse, Solve, NullSpace.

Further Examples