(Solved): A company makes 3 types of cable. Cable A requires 3 black wires, 3 white wires, and 2 red wires. ...

A company makes 3 types of cable. Cable A requires 3 black wires, 3 white wires, and 2 red wires. Cable \( B \) requires 1 black, 2 white, and 1 red. Cable \( C \) requires 2 black, 1 white, and 2 red. If 95 black wires, 100 white wires, and 85 red wires were used: a.) Set up a system of linear equations where \( x, y \), and \( z \) represent the number of Cable \( A, B \), and \( \mathrm{C} \) wires respectively. b.) Set up the system using Matrix Algebra notation \( (A X=B) \). Identify which matrix is \( A, X \), and \( \mathrm{B} \). c.) Find the Inverse of \( A \) using your calculator d.) Solve the system using Matrix Algebra (how many of each cable were made? )