Spanning 3D Space

Adjust the scaling factors s₁ and s₂. Notice that two vectors can only span a 2D plane within 3D space. Click and drag the graph to rotate the 3D view.

x₁ =
120
x₂ =
310

Linear Combination

s₁ = 1.0
s₂ = 1.0
z = 1.0
120
+ 1.0
310
=
4.03.00.0

All linear combinations z of x₁ and x₂ are confined to the xy plane because the third component is always 0.

Enjoying this visualization?

Get the full textbook:
Linear Algebra for Computer Science

3D View
Drag to rotate