Properties and Definitions of Matrices

Tuesday, 15 May 2018

1:14 PM

A system is said to be homogenous if the right hand side of the matrix row is zero

e.g.

 

An augmented matrix is one that only has the coefficients for each term

e.g. in

Matrix Representation:

 

A leading row is a row that is not all zero

 

A leading entry in a leading row is the left-most non-zero value

 

A leading column is a column which contains a leading entry

 

The row-echelon form of a matrix is the term given to when all leading rows are above all non-leading rows.

In every leading row, the leading entry is further to the right than any row higher up.

e.g.

 

The reduced row-echelon form of a matrix is one such that every leading entry is one, and that every leading entry is the only non-zero entry in its column.

e.g.

 

Gaussian elimination is the process of performing row operations to form a system in row-echelon form.

Further row operations can be performed to produce a reduced row-echelon form of a system

 

If  and  are solutions of , then so is  and