Finding the dimension of the Kernel $\mathbb{R}^{3*2} \rightarrow \mathbb{R}_4[x]$

Question

Approximate Question asked in Exam
You have an $\mathbb{R}^{3*2}$ matrix with linear transformation to $\mathbb{R}_4[x]$ (polynomial of degree $5$). Now you had to find the dimension of the Kernel.

I Choose an answer that said the The Dimension of the Kernel is $< 3$.
Is this correct?