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Math Help - Need help solving for this matrix

  1. #16
    Newbie
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    I first multiplied both sides by x^{T} which gave me

     x^{T}A^{T}Ax = x^{T}c
    Which simplifies to
     (Ax)^{T}(Ax) = x^{T}c
    and since we know that  ||Xy||^2 = \sqrt{(X \cdot y)} ^2
    then  || Ax || ^ 2 can be written as \sqrt{Ax \dcot Ax } ^2 which is Ax \cdot AX
    Also, we know that x \cdot y = x^{T}y so  Ax \cdot Ax = (Ax)^{T}Ax
    Therefore, since  (Ax)^{T}(Ax) = cx^{T} and  (Ax)^{T}Ax = || Ax || ^ 2 then || Ax || ^ 2 = x^{T}c = 2

    Thanks a ton for your help and fast responses. I'll definitely be coming back here in the future
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  2. #17
    A Plied Mathematician
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    Wow. There's a whole lot more there than there needs to be. Here's my solution:

    \|Ax\|^{2}=(Ax)^{T}(Ax)=(x^{T}A^{T})Ax=x^{T}(A^{T}  Ax)

    =\begin{bmatrix}1 &0 &2\end{bmatrix}\begin{bmatrix}2\\2\\0\end{bmatrix}  =2.
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