Question

What is the null space for a linearly independent system?

Answer 1

see below

Explanation:

If a system is linearly independent, it is invertible (and vice versa).

`M bb x = bb 0, qquad bbx ne bb 0`

`M^(-1) M bb x = M^(-1) bb 0`

`bb x = bb 0`

`implies N(M) = {bb 0}`

The null space contains only the zero vector and has nullity zero