Linear Algebra Dimensions of $\mathrm{Nul}(A)$ Suppose that $T \colon \mathbb{R}^3 → V$ is a linear transformation from $\mathbb{R}^3$ to some vector space $V$. Let $A$ represent the matrix of $T$. What are the possible dimensions of $\mathrm{Nul}(A)$? What would those dimensions mean geometrically?
The nullity of T depends upon the Codomain as well but the fact is it can't be greater than 3 due to sylvesters law of nullity
$NullA$ is exactly as solving $Ax = 0$. Which is exactly $KerT$. Thus, Its dim is smaller or equal to 3.