MATH 240 Lecture Notes - Lecture 1: Augmented Matrix, Solution Set, Matrix Multiplication

• School: University of Maryland
• Department: Mathematics
• Course: MATH 240
• Professor: Raluca Rosca

Document Summary

We will start by looking at systems of linear equations. There are three things: unknowns only appear in the numerator, the only powers are to the first power, no products or quotients of unknowns. Some examples of linear equations are equations like. Note that a solution set to an equation with two or more unknowns is infinite. We are however, not going to concern ourselves with those. Surely you know how to solve systems of equations. But in case you need a refresher, here"s an example. Let"s solve the first equation for y and then plug that into the second equation. (cid:889)(cid:1876)+(cid:884)(cid:1877)=(cid:883)(cid:888) (cid:884)(cid:1877)=(cid:883)(cid:888) (cid:889)(cid:1876) (cid:1877)=(cid:890) (cid:889)(cid:884)(cid:1876) Now let"s plug in y into the second equation. We expected the graph of these two lines to cross but they never do. That is why we got a nonsense answer and that is why this system has no solution!