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.
An example of a system of linear equations is
3x + 2y + 2z = 3
x + 2y - z = 5
2x - 4y + z = 0
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.
Click one of the following topics for more information:
Matrix Definitions
Determinant
RREF
Cramer's Rule
Internet references
A Brief History of Linear Algebra and Matrix Theory,
by Marie A. Vitulli
Related pages in this website
Linear Patterns -- a very basic
introduction to the concept of linear relationships
Vectors -- the "dot" product and
the "cross" product, explained.
