I have a interesting question about linear algebra problem. Assume that I have a matrix $A^{m \times n}$ and vector $c^{n \times 1}$ are known and I want to find the solution of vector y subject to $$Ay=c$$
The common method is Gaussian elimination. However, this method will find all element solution of vector y and take long time. My goal is that I find only single element $y_i$ of vector $y$, instead of find all element solution of $y=${$y_1,y_2....y_i..y_m$}. Could you suggest to me any way or method with low complexity to resolve my problem?
Thank you in advance