# Thread: u_1 and u_2 are two different sol. of Au=f

1. ## u_1 and u_2 are two different sol. of Au=f

Suppose $\displaystyle u_1$ and $\displaystyle u_2$ are different solutions of the same inhomogeneous linear equation $\displaystyle Au=f$. Find, in terms of $\displaystyle u_1$ and $\displaystyle u_2$, a family of solutions of this equation depending on an arbitrary constant.

I am not sure how to start.

2. Is $\displaystyle \displaystyle A$ a constant? Are $\displaystyle \displaystyle f,u$ functions of $\displaystyle \displaystyle x$?

3. Hi dw, this seems quite general and probably the reason you can't get started.

Are you are looking for $\displaystyle u = A^{-1}f$ ?

Take a look at posts #8,11,12,13. See if anything you are studying is firmilar.

http://www.mathhelpforum.com/math-he...ial-38182.html

4. To Prove it, u is usually a function of x and y i.e. u(x,y). I have no idea what f is but I am thinking it is a function of x and y, f(x,y). A is a linear operator.

To pickslides, I am not sure what I am looking for.

This is the introduction section to Linear Operators.