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

• Dec 29th 2010, 04:40 PM
dwsmith
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.
• Dec 29th 2010, 05:40 PM
Prove It
Is \$\displaystyle \displaystyle A\$ a constant? Are \$\displaystyle \displaystyle f,u\$ functions of \$\displaystyle \displaystyle x\$?
• Dec 29th 2010, 05:42 PM
pickslides
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
• Dec 29th 2010, 05:52 PM
dwsmith
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.