Section 1.2 Terminology and notation
- linear equation
-
an equation of the form
\begin{equation*} \text{number times variable plus number times variable plus }\dots \text{ equals number} \end{equation*} - system of linear equations
a (finite) collection of linear equations
Note 1.2.1.
We will often just say system of equations to mean a system of linear equations.
- solution
a set of values that, when substituted in for the variables of a system of equations, satisfy all of the equations in the system simultaneously
- solution set
the collection of all possible solutions to a system of equations
- consistent system
a system of equations with at least one solution
- inconsistent system
a system of equations with no solution
- parametric equations
a collection of formulas, based on one or more parameters, for the variables in a linear system that represent all possible solutions to the system (as the parameters vary over all real numbers)
- matrix
a rectangular array of numbers
- augmented matrix
a matrix of the coefficients and constants in a linear system
- matrix entry
one of the numbers in a matrix; sometimes also referred to as a matrix coefficient
- row
a horizontal line of entries in a matrix
- column
a vertical line of entries in a matrix
- elementary row operations
-
the three basic operations that can be applied to an augmented matrix without changing the set of solutions to the corresponding linear system:
- swap the positions of two rows,
- multiply a row by a nonzero constant, and
- add a multiple of one row to another.