Math 240 Homework Assignment One Do the following problems showing all your work. Be sure to submit your solutions in PDF format to the Assignment area of LEO. (Point values are given in the square brackets.) 1. [5] Use elimination to find all solutions of the system: + 2 + 3 = 1 2 + 4 + 7 = 2 3 + 7 + 11 = 8 2. [5] Find all the solutions of the linear system, + 2 + 3 = + 3 + 8 = + 2 + 2 = where a, b, and c are arbitrary constants. (We say this system is \"parameterized\" by a, b and c.) 3. [5] Use \"pencil and paper\" with Gaussian elimination to solve the system, 2! 3! + 7! + 7! = 0 2! + ! + 6! 6! 12! = 0 ! 3! + ! + 5! = 0 2! + ! + ! + ! = 0 2! + ! 3! + 8! + 7! = 0 4. [5] Find a polynomial of degree three (that is, a polynomial of the form = + + ! + ! ) whose graph goes through the points 0,1 , 1,0 , 1,0 , and 2, 15 . Sketch a graph (or use an app) of this cubic. 5. [5] \"A duck costs four coins, five sparrows cost one coin, and a rooster costs one coin. Somebody buys 100 birds for 100 coins. How many of each kind of bird can he buy?\