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Thread: Need help solving for this matrix

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

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

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

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