matinverseimage

Function: matinverseimage
Section: linear_algebra
C-Name: inverseimage
Prototype: GG
Help: matinverseimage(x,y): an element of the inverse image of the vector y
 by the matrix x if one exists, the empty vector otherwise.
Doc: given a matrix $x$ and
 a column vector or matrix $y$, returns a preimage $z$ of $y$ by $x$ if one
 exists (i.e such that $x z = y$), an empty vector or matrix otherwise. The
 complete inverse image is $z + \text{Ker} x$, where a basis of the kernel of
 $x$ may be obtained by \kbd{matker}.
 \bprog
 ? M = [1,2;2,4];
 ? matinverseimage(M, [1,2]~)
 %2 = [1, 0]~
 ? matinverseimage(M, [3,4]~)
 %3 = []~    \\@com no solution
 ? matinverseimage(M, [1,3,6;2,6,12])
 %4 =
 [1 3 6]

 [0 0 0]
 ? matinverseimage(M, [1,2;3,4])
 %5 = [;]    \\@com no solution
 ? K = matker(M)
 %6 =
 [-2]

 [1]
 @eprog