I'm taking a finite mathematics course and most recently we learned about matrices. We've been discussing Gauss-Jordan Elimination and terminology. I was doing my homework and having a pretty easy time of it until given a matrix and being asked to find the linear equation it represented and show the solution. Here:
[1 -2 0 -3 | -5] = x1 - 2x2 -3x4 = -5 The confusion I had was what solution I was supposed to show.
[0 0 1 3 | 2] = x3 + 3x4 = 2 There are four variables and only two equations.
My husband teaches math in high school so I figured he could help. As he had me point out, x4 is present in both equations. Therefore, it becomes t. Okay, simple enough. So then we say x3 = -3t + 4. Okay, still good. But now what do we do with x1 and x2 ? As we all know, solving for one variable is easier than two so we say x2 (or x1) is s. So x1 = 2s - 3t -5 and we're done. I say to hubby, "It all seems so arbitrary. How can you assign random letters to different variables and retain some meaning?" This is how he explains it:
"Say we have PS2's, PS3's, PS4's, and Xbox's and we want to find out how many we need to sell of each to get a specific sales figure. If we say that 5000 Xbox's were sold, does that guarantee that 400 PS4's sold? No, so we assign a value t. We then say that another console, PS3's is represented by s. It's not arbitrary because we're accounting for the many real numbers that could be the values for the four variables."
I'm paraphrasing, since he definitely did not use those words exactly, but you get the gist. I was like, "That makes so much more sense when you put it that way". If I didn't have to go to my Statistics class immediately upon finishing Finite, I might have been able to ask my professor, but he doesn't know me personally and know what context would make sense to me. That and my husband is a great teacher.
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