# Prove the following identity

• Dec 20th 2011, 09:36 AM
FGT12
Prove the following identity
Show that for $\displaystyle A \in M_n(\mathbb{R})$ and $\displaystyle x,y \in \mathbb{R}^n$

$\displaystyle x \cdot Ay = y \cdot Ax$

I get
$\displaystyle y \cdot Ax = y^t Ax$ but i cannot see where to go now

I think it may involve $\displaystyle (AB)^t=B^tA^t$
• Dec 20th 2011, 10:05 AM
ILikeSerena
Re: Prove the following identity
Hi FGT12! :)

You're on the right track.
Can you say what $\displaystyle (y^tAx)^t$ is?
• Dec 20th 2011, 12:18 PM
Opalg
Re: Prove the following identity
Quote:

Originally Posted by FGT12
Show that for $\displaystyle A \in M_n(\mathbb{R})$ and $\displaystyle x,y \in \mathbb{R}^n$

$\displaystyle x \cdot Ay = y \cdot Ax$

I get
$\displaystyle y \cdot Ax = y^t Ax$ but i cannot see where to go now

I think it may involve $\displaystyle (AB)^t=B^tA^t$

There is a missing$\displaystyle {\color{white}.}^t$ somewhere. It should be $\displaystyle x \cdot A^ty = y \cdot Ax$. Either that, or there is a missing condition $\displaystyle A^t=A.$