Problem 2 (Linear algebra refresher) (10 points) In the "Harry Potter" series, wizards have their own currency system consisting of Galleons, Sickles, and Knuts. In Harry Potter and the Sorcerer's Stone, Rubeus Hagrid tells Harry that there are 17 Sickles to a Galleon, and 29 Knuts to a Sickle. Additionally, J. K. Rowling has stated that USD $250,000,000 is equivalent to 34,000,872 Galleons, 14 Sickles, and 7 Knuts. Suppose you want to determine the worth of each wizard currency (Galleon, Sickle, and Knut) in USD. (a) Using the given information, write down a system of three linearly independent equations for the unknown values.