Span of two vectors

Span of two vectors: linear algebra practice

Determine the geometric size and location of the span of two vectors. Coordinate examples and general reasoning distinguish a whole plane from a line or the zero space. You will also describe a generated plane using a relation among coordinates, providing a bridge between combinations and geometric constraints.

What you will practise

• Classify the set generated by two vectors as a plane, line or zero space
• Use a parametric description to identify the generated plane
• Recognize how dependence and zero generators change the geometry

How to use this questionset

Prerequisites: Span, scalar multiples and non-collinear directions. The questions progress from direct interpretation to application and reasoning. Work out an answer before comparing the choices; for multi-select questions, evaluate every statement independently. Worked explanations show the reasoning and address relevant misconceptions, so an incorrect attempt can guide your next review.

All spans pass through the origin. Two generators do not automatically provide two distinct directions. This classification supports independence and later parametric equations of planes. This microlearning belongs to Module 1, Vectors and Geometry, in the Complete Linear Algebra Course.