Do we have to know Cramer's rule for the exam?
March 3, 2010 2:20 PM Subscribe
Why do people care about Cramer's rule?
posted by leahwrenn to Education (8 answers total) 4 users marked this as a favorite
OK, so I'm teaching linear algebra again, and this time I have lots of engineering students in my class, all of whom apparently are taught to use Cramer's rule to solve systems of equations [apparently derived from...some stuff...using some Laplace transforms or something. They're not totally clear and I don't do that kind of math much] and who are interested in seeing something about it in the (very pure math-y) linear algebra course they're required to take.
So, my question is why are they being taught to use Cramer's rule, instead of just row-reducing a matrix? Even for systems derived from Laplace transforms, where you've got some parameter in the coefficients, a computer algebra system should be able to row-reduce the matrix just fine (Mathematica doesn't seem to care), and for general solving of linear systems, row-reduction is cheap and easy (and has the advantage that it works even when you don't have an n x n system). Is it that back in the day, Cramer's rule was so much easier for hand-computation, and so that's just the way they've always done it? Or is there a way/situation in which using Cramer's rule really is computationally cheaper, in practice (as opposed to toy exam questions)?
In fact, any insights people have about how/whether engineers actually use Cramer's rule "in real life" would be appreciated.
Also, I have heard (and vaguely remember) there are places in which Cramer's rule really is useful theoretically. Any good examples folks have floating around?