Systems of linear equations can be solved using "matrix math". This
section explains some of these techniques.
Matrix Definitions define order
and rank, scalar and matrix multiplication, properties (such as
associative, commutative), etc.
The "Determinant" is a scalar value
obtained by algebraically summing products of cells in different rows and
columns. This page explains it, gives an algorithm to find it, and
tells you why it is useful.
RREF is "Reduced Row Echelon
Form" a.k.a. Gauss-Jordan elimination: a way of solving a system of
linear equations.
Cramer's Rule is another way of
solving a system of linear equations, especially useful if you have a
quick way of getting the determinant of a matrix.
A traditional way of solving this is to multiply pairs of equations through
by different numbers so they can be added together to eliminate variables.
This method is tedious, but it can be automated by observing that certain types
of matrix manipulation give the same results.