# Math Help - Need help solving for this matrix

1. 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

2. 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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