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
© 1996-9 Eric W. Weisstein
1999-05-26