1. You are given a linear system: Ax = b where A is an n x n invertible matrix. Consider finding the solutions x in the following ways. How many operations ('flops') are required in each case as a function of n? You only need to give the highest-order term ( do not use big-O notation).

a. by finding the reduced row-echelon form of the augmented matrix [A b].

b. by computing A^-1 and solving via x = A^-1(b).

2. A company produces two products: potatoes and carrots. To produce a potato, the company spends 7 cents on materials, 14 cents on labor, and 3 cents on overhead. To produce a carrot, the company spends 8 cents on materials, 17 cents on labor, and 1 cent on overhead. In one day, the company finds that it has spent $2.27 on materials, $4.71 on labor, and $0.56 on overhead. How many pencils and how many markers did the company produce that day? Show your work.