PROBLEM $01$: Linear and Cyclic Convolutions

$1$a$.25$ Points.$-$ Obtain the linear convolution of the sequences below:

$x[n]=e^{+j\frac{2}{4}n}+e^{-j\frac{2}{4}n},nin{Z}_4$

$h[n]=[n-2],nin{Z}_5$

$y[n]={\displaystyle \underset{k=0}{\overset{k=1}{}}}x[k]h[n-k]={\displaystyle \underset{k=0}{\overset{k=2}{}}}h[k]x[n-k],nin{Z}_8$

Use a matrix$-$vector product operation to perform your computation.