5)there is $\displaystyle f:R^{n}xR^{n}->R$ which is defined by $\displaystyle f(x,y)=n\sum_{i=1}^{n}(x_{i}-m_{x})(y_{i}-m_{y})$ where

$\displaystyle m_{y}=\frac{y_{1}+..+y_{n}}{n}$

$\displaystyle m_{x}=\frac{x_{1}+..+x_{n}}{n}$

$\displaystyle x=(x_{1}+..+x_{n}) y=(y_{1}+..+y_{n})$

A)check if this function is a simetric bilenear.

B)find the representative matrices by the standart basis of $\displaystyle R^{n}$

C)find the jordan form of the matrices you found in part B

D)check if $\displaystyle n||x||^{2}>=f(x,x)>=0$ for every $\displaystyle x\in R^{n}$

??

regarding A:

f is simetric if f(x,y)=f(y,x) so i need to prove that

$\displaystyle f(x,y)=n\sum_{i=1}^{n}(x_{i}-m_{x})(y_{i}-m_{y})=n\sum_{i=1}^{n}(y_{i}-m_{y})(x_{i}-m_{x})=f(y,x)$

but when i put the given $\displaystyle m_{y}$and $\displaystyle m_{x}$ i get two different expressions

?