I came across a problem while programming. Given the matrices A and B, I need a specific row from the matrix $H=A^{-1}B$, but I don't want to find $A^{-1}$ given the computational cost. I know I can find any column of $H$ with a simple system of equations, but I can't find a similar formula for a row. So, is there a way to find the nth row of matrix H with a simple system of equations? I know that, since $AH=B$ , I can compute H by H=B\A in Matlab, but is there a way to calculate a row without computing $H$ completely.
Thank you!