Use an Inverse Matrix to Find the Solution to the System

Multiple Choice

Use an inverse matrix to find the solution to the system.
-Suppose that in a certain city, the Democratic, Republican, and Independent parties always nominate candidates mayor. It turns out that the percent of people voting for each party candidate in the next election depends on the that voted for that party in the last election. The percent voting for each party in the next election is given by
$$\left[ \begin{array} { l } \mathrm { D } \\\mathrm { R } \\\mathrm { I }\end{array} \right] = \left[ \begin{array} { l l l } 60 & 20 & 30 \\30 & 60 & 30 \\10 & 20 & 40\end{array} \right] \left[ \begin{array} { l } \mathrm { d } \\\mathrm { r } \\\mathrm { i }\end{array} \right]$$
where $\mathrm { d } , \mathrm { r }$ , and $\mathrm { i }$ are the respective percents (in decimals) that voted for that party in the last election. If the perce voting for a Democrat in the next election is $41 \%$ , the percent voting for a Republican in the next election is $42 \%$ , and the percent voting for the Independent party in the next election is $17 \%$ , then what percent of people voted for an Independent in the last election?

A) 40%
B) 50%
C) 10%
D) 25%