Let $k$ be an algebrically closed field and let $l\colon \mathbb{A}^m_k\rightarrow\mathbb{A}^n_k$ be a one to one morphism of affine variety given by a matrix that maps $x$ to $A[x]$, here $A$ is a matrix. How I can prove that image of $l$ is closed.
I do not want to use the general theorem which says every morphism of projective varieties has closed image.
If you can please help since its some day that I can not prove it.