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

**dwsmith** · December 29th 2010, 04:40 PM

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

I am not sure how to start.

**Prove It** · December 29th 2010, 05:40 PM

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

**pickslides** · December 29th 2010, 05:42 PM

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

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

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

**dwsmith** · December 29th 2010, 05:52 PM

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.

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