A linear equation in n unknowns is an equation of the form a₁x₁+a₂x₂+. . .+a_nx_n=b where a₁,a₂,...,a_n and b are variables, and x₁,x₂,...,x_n are real numbers.

A system is consistent if it has at least one solution.

A system is inconsistent if it has at least two solutions.

The following system is a linear system:
x+y=2
2x-.3y=0

Two systems of equations involving the same variables are said to be equivalent if they have the same solution set.

A system is in triangular form if in the kth equation the first k-1 coefficients are nonzero and the coefficient of x_k and all the following x_i's are zero.

A matrix is a rectangular array of numbers.

If a matrix has n columns and m rows, we say it is n by m.

"Multiply a row by zero" is an elementary row operation.

"Interchange two rows" is an elementary row operation.