In matrix form,

$\left[y_{p}(n)\right]_{4 \times 1}=\left[x_{p}(n)\right]_{4 \times 4}\left[h_{p}(n)\right]_{4 \times 1}$

$\left[\begin{array}{c}{y_{p}(0)} \\ {y_{p}(1)} \\ {y_{p}(2)} \\ {y_{p}(3)}\end{array}\right]=\left[\begin{array}{cccc}{x_{p}(0)} & {x_{p}(3)} & {x_{p}(2)} & {x_{p}(1)} \\ {x_{p}(1)} & {x_{p}(0)} & {x_{p}(3)} & {x_{p}(2)} \\ {x_{p}(2)} & {x_{p}(1)} & {x_{p}(0)} & {x_{p}(3)} \\ {x_{p}(3)} & {x_{p}(2)} & {x_{p}(1)} & {x_{p}(0)}\end{array}\right] \times\left[\begin{array}{c}{h_{p}(0)} \\ {h_{p}(1)} \\ {h_{p}(2)} \\ {h_{p}(3)}\end{array}\right]$

$=\left[\begin{array}{llll}{1} & {2} & {1} & {2} \\ {2} & {1} & {2} & {1} \\ {1} & {2} & {1} & {2} \\ {2} & {1} & {2} & {1}\end{array}\right] \times\left[\begin{array}{l}{4} \\ {0} \\ {4} \\ {0}\end{array}\right]$

$=\left[\begin{array}{l}{4+0+4+0} \\ {8+0+8+0} \\ {4+0+4+0} \\ {8+0+8+0}\end{array}\right]$

$\left[\begin{array}{l}{y_{p}(0)} \\ {y_{p}(1)} \\ {y_{p}(2)} \\ {y_{p}(3)}\end{array}\right]=\left[\begin{array}{c}{8} \\ {16} \\ {8} \\ {16}\end{array}\right]$