Let a linear system of equations be denoted

(1) 
where
is a Matrix and X and Y are Vectors. As shown by Cramer's Rule,
there is a unique solution if
has a Matrix Inverse
. In this case,

(2) 
If
, then the solution is
. If
has no Matrix Inverse, then the solution
Subspace is either a Line or the Empty Set. If two equations are multiples of each other, solutions
are of the form

(3) 
for a Real Number.
See also Cramer's Rule, Matrix Inverse
© 19969 Eric W. Weisstein
19990526