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

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

    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.
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  2. #2
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    Is \displaystyle A a constant? Are \displaystyle f,u functions of \displaystyle x?
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  3. #3
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    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
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  4. #4
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    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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