8. Three investors $I_1, I_2$, and $I_3$ each have a stock portfolio consisting of the same four stocks $S_1, S_2, S_3$, and $S_4$. Let a "quantity matrix" be $Q = [q_{ij}] = \begin{bmatrix} 18 & 26 & 4 & 1 \\ 5 & 2 & 9 & 53 \\ 10 & 17 & 26 & 33 \end{bmatrix}$ where $q_{ij}$ = the number of shares of stock $S_j$ held by investor $I_i$ throughout all of 2014.
(a) Assume the value in $CAD of $S_j$ at the end of the $n^{th}$ day of 2014 is $w_j(n)$. Let $W(n)$ be the column matrix with entries $w_j(n)$. Find and interpret the meaning of $QW(n)$. [7 points]
(b) On August 13, 2014 (the $225^{th}$ day of 2014) the American/Canadian dollar exchange rate is 1 $US = 1.09 $CAD. State the matrix $A$ so that the entries in the product $AQW(225)$ represent the average value of each investor's stock portfolio on August 13, 2014 in $US. [4 points]
(c) Suppose that $R$ represents a revised quantity matrix for all of 2015 where, compared to 2014, each investor has 2 more units of $S_1$, 10% less of $S_2$, the same amount of $S_3$, and 5% more of $S_4$. If $P + Q = R$, find $P$. [5 points]
