# LinearSystemMatrixPackage1 FΒΆ

- F: Field

This package solves linear system in the matrix form `AX = B`

. It is essentially a particular instantiation of the package LinearSystemMatrixPackage for Matrix and Vector. This package`'s`

existence makes it easier to use solve in the FriCAS interpreter.

- hasSolution?: (Matrix F, Vector F) -> Boolean
`hasSolution?(A, B)`

tests if the linear system`AX = B`

has a solution.

- particularSolution: (Matrix F, Vector F) -> Union(Vector F, failed)
`particularSolution(A, B)`

finds a particular solution of the linear system`AX = B`

.

- rank: (Matrix F, Vector F) -> NonNegativeInteger
`rank(A, B)`

computes the rank of the complete matrix`(A|B)`

of the linear system`AX = B`

.

- solve: (List List F, List Vector F) -> List Record(particular: Union(Vector F, failed), basis: List Vector F)
`solve(A, LB)`

finds a particular soln of the systems`AX = B`

and a basis of the associated homogeneous systems`AX = 0`

where`B`

varies in the list of column vectors`LB`

.

- solve: (List List F, Vector F) -> Record(particular: Union(Vector F, failed), basis: List Vector F)
`solve(A, B)`

finds a particular solution of the system`AX = B`

and a basis of the associated homogeneous system`AX = 0`

.