# Question about solving linear equations

I have two questions here.

Suppose $A \in \mathbf{C}^{k \times k}$ and $B \in \mathbf{C}^{k \times l}$, I want to solve the equation $$AT=B$$ to within an accuracy of $\epsilon$. Which numerical method should I use?

If $A$ is ill-conditioned, there is a large set of solutions. How could I pick one for which $\|T\|_F$ is minimized. $\|T\|_F$is Frobenius norm of the matrix