# LinearSystemMatrixPackage1 F¶

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.
solve: (Matrix 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: (Matrix 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.