# Thread: Determine nullity when matrix power =0

1. ## Determine nullity when matrix power =0

If M^(n-1) notequal 0 but $, M^n=0$, then determine dim ker (M)

I feel the following two equations and rank nullity theorem can be used for this but not sure how

2. ## Re: Determine nullity when matrix power =0

Let $x$ such that $M^{n-1}x\neq 0$. Show that the vectors $x,Mx,\ldots,M^{n-1}x$ are linearly independent. Therefore, the family $\mathcal B=\{M^jx\}_{0\leq j\leq n-1}$ is a basis of the vector space in which we are working. Write the endomorphism associated to $M$ in the basis $\mathcal B$.