LinearSolve

LinearSolve(matrix, right)

solves the linear equation system matrix . x = right and returns one corresponding solution x.

See

• Wikipedia - System of linear equations - Solving a linear system

Examples

>> LinearSolve({{1, 1, 0}, {1, 0, 1}, {0, 1, 1}}, {1, 2, 3})
{0,1,2}

Test the solution:

>> {{1, 1, 0}, {1, 0, 1}, {0, 1, 1}} . {0, 1, 2}
{1,2,3}

If there are several solutions, one arbitrary solution is returned:

>> LinearSolve({{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}, {1, 1, 1})
{-1,1,0}

Infeasible systems are reported:

>> LinearSolve({{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}, {1, -2, 3})

LinearSolve({{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}, {1, -2, 3})

Argument {1, {2}} at position 1 is not a non-empty rectangular matrix.

>> LinearSolve({1, {2}}, {1, 2})
LinearSolve({1, {2}}, {1, 2})

>> LinearSolve({{1, 2}, {3, 4}}, {1, {2}})
LinearSolve({{1, 2}, {3, 4}}, {1, {2}})

Implementation status

• ✅ - full supported

Github

• Implementation of LinearSolve