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

zero matrix is in reduced row-echelon form

The homogeneous linear system has only two possibilities for its solutions

The homogeneous linear system can only have a trivial solution

The homogeneous linear system can have nontrivial solutions

The homogeneous linear system can have no solution

in scalar multiplication we multiply a row vector by a column vector

when we multiply a number to a matrix of linear system, we multiply it to either one row or one column

To multiply two matrices A and B, the number of columns of A must be the same number of rows of B

The resulting matrix for multiplying A and B has the same number of rows as A and the same number of columns as B

With matrices, multiplication is not commutative