if A is invertible then AX = b has exactly one solution namely A^-1 .b

if A isn’t invertible, then AX = b has either infinite solutions or no solutions

(A^-1)^-1 =

(5A)^-1 = 1/5 A^-1

(AB)^-1 =

if a product AB isn’t invertible then A or B isn’t invertible

if A or B isn’t invertible then AB isn’t invertible

ax + by = c          ( a ≠ 0 or b ≠ 0 ) is an example of linear equation in Three-dimensional

linear equation can involve products or roots of variables

all variables in linear equations occur only to the first power and don't appear

aij in a linear system, the ……. subscript indicates the equations in which the coefficient occurs and the …….indicates which unknowns it multiplies.

We say that a linear system is inconsistent If it has at least one solution

We say that a linear system is ……. If it has at least one solution and …….. if it has no solutions

in inconsistent linear systems may have either one solution or infinitely solution – there is no other possibilities.

if two lines/ plans in linear system has intersection in a line, you will not have many solutions to this linear system

for the following linear system, first equation: x + y = 1  , second equation: 2x + 2y = 5    there is

for the following linear system, first equation: x + y = 1  , second equation: 4x + 4y = 4    there is

Performing algebraic operations on the system alter the solution set

A homogeneous system always has at least one solution

In EchelonForms, if there are any rows consists entirely of zeros, they are groubed at the top of the matrix

A matrix in reduced row-echelon form is of necessity in row-echelon form and vice versa