This is a reference request, I would like to know where to find results concerning the inverse of a matrix: Suppose we have the matrix $A \in \mathbb{R}^{n\times n}$ and a vector $b$. We consider $x = A^{-1}b$. If we now change the last row $a \in \mathbb{R}^n$ of $A$, how does $x$ change? More specifically, if we exchange $a$ by $b$ such that the Euclidean distance between $a$ and $b$ is strictly greater than some constant $c > 0$, how does this change $x$?
I am interested in any sort of result concerning this type of linear algebra, I would also appreciate references to articles that use linear algebra from a more geometric point of view.
Many thanks.