Abstract: The talk will focus on issues related to the problem of solving the matrix equation
Ax=y
where A is an $ m x n$ matrix with real or complex entries. We shall see that even if the above equation does not have a solution,the corresponding normalized equation
A*Ax=A*y
always has a solution, where A* is the conjugate transpose of A. We see that, the problem of obtaining such a solution with a minimum norm can be ill-conditioned. We shall indicate that solution of ill-condioned systems naturally arise while solving ill-posed inverse problems of practical interest.