Let period of $x_{1}(n)$ and $x_{2}(n)$ be 5

$x_{1}(n)=\{1,-1,-2, 3,-1\} \ and\ \quad x_{2}(n)=\{1,2,30,0\}$

In matrix form, $[y(n)]_{5 \times 1}=\left[x_{1}(n)\right]_{5 \times 5}\left[x_{2}(n)\right]_{5 \times 1}$

$\left[\begin{array}{c}{y(0)} \\ {y(1)} \\ {y(2)} \\ {y(3)} \\ {y(4)}\end{array}\right]=\left[\begin{array}{cccccc}{x_{1}(0)} & {x_{1}(4)} & {x_{1}(3)} & {x_{1}(2)} & {x_{1}(1)} \\ {x_{1}(1)} & {x_{1}(0)} & {x_{1}(4)} & {x_{1}(3)} & …