# What is the null space for a linearly independent system?

Jun 8, 2018

see below

#### Explanation:

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

$M \boldsymbol{x} = \boldsymbol{0} , q \quad \boldsymbol{x} \ne \boldsymbol{0}$

${M}^{- 1} M \boldsymbol{x} = {M}^{- 1} \boldsymbol{0}$

$\boldsymbol{x} = \boldsymbol{0}$

$\implies N \left(M\right) = \left\{\boldsymbol{0}\right\}$

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