Exercise 5

Find the nullity of each map below.

• (a)  $h\colon\mathbb{R}^{5}\to\mathbb{R}^{8}$ of rank five     (b)  $h\colon\mathcal{P}_{3}\to\mathcal{P}_{3}$ of rank one     (c)  $h\colon\mathbb{R}^{6}\to\mathbb{R}^{3}$, an onto map     (d)  $h\colon\mathcal{M}_{3\!\times\!3}\to\mathcal{M}_{3\!\times\!3}$, onto