1)Given a circular matrix

A=\begin{bmatrix}
a& b& c\\
c& a& b\\
b& c& a
\end{bmatrix}


B=\begin{bmatrix}
e& f& g\\
g& e& f\\
f& g& e
\end{bmatrix}



1) Show that C=AB is also a cicular matrix. Write the form of a circular matrix 4x4.

* I have done this part

2) Show the vector x1= \left[1 1 1 \right ]T satisfy the linear equations A x1 = \Lambda 1 x1

*This part also has been done

3) For the vector x1 in part 2 find the corresponding value of \Lambda1
*I guess this part also have been solved.

Now here is my question, instead of x1=\left[1 1 1 \right ]Tnow the vector x1 is replace by x1 = \left [1, -\frac{1}{2}+\frac{\sqrt{}3}{2}j,-\frac{1}{2}-\frac{\sqrt{}3}{2}j \right ]T



Lets assume the value for x1 is the same for the left and right side.
How do we do part 2 and 3 if we use x1 = \left [1, -\frac{1}{2}+\frac{\sqrt{}3}{2}j,-\frac{1}{2}-\frac{\sqrt{}3}{2}j \right ]T[/QUOTE]