In the financial pages of a newspaper, one can sometimes find a table (or matrix) listing the exchange rates between currencies. In this exercise we will consider a miniature version of such a table, involving only the Canadian dollar (C$) and the South African Rand (ZAR). Consider the matrixC$ ZARA =1/8 1C$ ZAR representing the fact that C$1 is worth ZAR8 (as of June 2008). a. After a trip you have C$100 and ZAR 1,600 in your pocket. We represent these two values in the vector 100 1,600 . Compute Ax. What is the practical significance of the two components of the vector Ax? b. Verify that matrix A fails to be invertible. For which vectors b is the system Ax = b consistent? What is the practical^ significance of your answer? If the system Ax = b is consistent, how many solutions jc are there? Again, what is the practical significance of the answer?

Math 121 Chapter 2 Notes Lesson 2.2 – Linear Inequalities in One Variable Example 1. 3x – 4 ≥9 + 5x (Add 4 and subtract 5x from both sides.) -2x ≥ 13 (Divide both sides by -2 and flip the sign.) x ≤ -6.5 Interval notation: (-∞, -6.5] (On a number line, a solid mark would be on -6.5 and point toward negative infinite.) Example 2. -24 < 3x – 3 ≤ 18 (Add 3 to all sides of the equation and divide by 4 to isolate the x in the middle.) -7 < x ≤ 7 (On a number line, this would look like an