Systems of Linear Equations: Three Variables

Flashcards covering key vocabulary and concepts from the lecture on systems of linear equations with three variables.

Solution Set

An ordered triple (x, y, z) representing the intersection of three planes in space.

Inconsistent System

A system of equations in three variables is inconsistent if no solution exists, often resulting in a contradiction after elimination operations.

Dependent System

A system of equations in three variables is dependent if it has an infinite number of solutions, resulting in an identity after elimination operations.

Elimination Operations

Steps used to solve a system of equations that may include interchanging equations, multiplying by a nonzero constant, and adding multiples of equations.

Intersection of Planes

The point or line where three planes in a space meet, represented by the ordered triple (x, y, z).

Parallel Planes

Planes that never intersect and can lead to an inconsistent system in three-variable equations.

Identity

A true statement resulting from elimination operations indicating a dependent system with an infinite number of solutions.

Intersection at a Line

A situation in a dependent system where three planes intersect along a straight line.