# Thread: Need help solving for this matrix

1. 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

2. 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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