# How to inverse $(I + \alpha M)$ for all $\alpha$ [duplicate]

I am looking for a way to solve the following equation:

$$(I + \alpha M)X=F$$

$$\forall \alpha \in R$$ (the real domain), with $$M$$ a square complex matrix without any particular properties, $$I$$ the identity matrix, $$F$$ a complex vector and $$X$$ the unknown.

Thank you,

• Suppose $\alpha=-1$ and $M=I$. – John Douma Oct 29 '18 at 22:33