solve (Matrix)

Solves a system of linear equations xM=b. If it is solvable,

returns such that (1/D)*x is the solution. If the system is not solvable, returns such that c*M^T = <0> and b c dot =/= 0

Arguments

Coefficient

(see Matrix).
of free terms (see Vector).

Return values

is a Vector of values that after dividing by satisfy the system of equations, empty if the system is not solvable.
is a real number to divide the by to get the solution, empty value if not solvable.
of the coefficient matrix if the system is solvable, empty otherwise (see Vector).
is TRUE if the system is solvable, FALSE otherwise.

Complexity

O(size^3)

Example

"sl/algebra" useFile checkedSolve: [ m:v:;; m v solve [ drop d:; res:; "factor: " print d print LF print res.makeRange [print "," print] each LF print ] [ fv:; drop drop "fail, v: " print fv.makeRange [print "," print] each LF print ] if ] func; m1: ((2.0 1.0 1.0) (-5.0 1.0 2.0) (-1.0 0.666666 1.0)) makeMatrix; m2: ((3.0 1.0) (1.0 2.0) (2.0 1.0)) makeMatrix; m1 (1.0 3.0 2.0) makeVector checkedSolve m1 (-8.0 3.0 5.0) makeVector checkedSolve m2 (1.0 1.0) makeVector checkedSolve
Output: