An electronics company has several hundred employees with two types of meal arrangements: bringing meals from home or eating out. Long-term surveys have found that: if an employee brings meals from home on a given day, then $10\%$ will switch to eating out the next day; if an employee eats out on a given day, then $20\%$ will switch to bringing meals from home the next day. Let $x _ { 0 }$、$y _ { 0 }$ respectively represent the proportion of employees bringing meals from home and eating out today relative to the total number of employees, where $x _ { 0 }$、$y _ { 0 }$ are both positive, and $x _ { n }$、$y _ { n }$ respectively represent the proportion of employees bringing meals from home and eating out after $n$ days relative to the total number of employees. Given that the number of employees in the company remains unchanged, select the correct options.
(1) $y _ { 1 } = 0.9 y _ { 0 } + 0.2 x _ { 0 }$
(2) $\left[ \begin{array} { l } x _ { n + 1 } \\ y _ { n + 1 } \end{array} \right] = \left[ \begin{array} { l l } 0.9 & 0.2 \\ 0.1 & 0.8 \end{array} \right] \left[ \begin{array} { l } x _ { n } \\ y _ { n } \end{array} \right]$
(3) If $\frac { x _ { 0 } } { y _ { 0 } } = \frac { 2 } { 1 }$ , then $\frac { x _ { n } } { y _ { n } } = \frac { 2 } { 1 }$ holds for any positive integer $n$
(4) If $y _ { 0 } > x _ { 0 }$ , then $y _ { 1 } > x _ { 1 }$
(5) If $x _ { 0 } > y _ { 0 }$ , then $x _ { 0 } > x _ { 1 }$

Let $A = \left[ \begin{array} { l l } 1 & 2 \\ 0 & 3 \end{array} \right]$. If $A ^ { 4 } = \left[ \begin{array} { l l } a & b \\ c & d \end{array} \right]$, what is the value of $a + b + c + d$?
(1) 158
(2) 162
(3) 166
(4) 170
(5) 174

Let matrix $A = \left[\begin{array}{cc} 1 & 1 \\ 1 & -1 \end{array}\right]$. If $A^{7} - 3A = \left[\begin{array}{ll} a & b \\ c & d \end{array}\right]$, then which of the following is the value of $a + b + c + d$?
(1) $-8$
(2) $-5$
(3) $5$
(4) $8$
(5) $10$