Linear dependence and the null space

When a vector lies in the span of two others, shown in 3D, and the null space of a 2 × 2 matrix as the line it sends to the origin.

Figure 2.1.Drag the 3D picture to rotate it, and move a, b and h to build C. In the second part, edit the matrix or press Play; the yellow line is the null space. Open on its own

Linear dependence is a property of the whole set: three vectors can be dependent even when no two of them are parallel.

rank + nullity = number of columns.