problem 2 linear algebra refresher 12 points in the harry potter serie

Question

Problem 2 (Linear algebra refresher) (12 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. (b) Convert said system into a matrix equation of the form [A]\{x\}=\{b\} where [A] is a 3 x 3 matrix of known numbers, {x} is a 3 x 1 matrix of unknowns, and {b}is a 3 x 1 matrix of known numbers. (c) Solve (1) for the worth of each currency.