Cramer's rule question

[becomingagodo]

Do you use cramer's rule? or is it a waste of time. I just wanted to know what advantages you have using cramer's rule? The only reason I can see is if your bad with fractions, however can't you just get rid off them.

I really don't won't to learn something if it is a waste of time.

[drkitten]

Do you use cramer's rule? or is it a waste of time.

I really don't won't to learn something if it is a waste of time.

With that attitude, I'd begin by suggesting that for you, learning anything might well be a waste of time.

Basically, if you can take the determinant of a system faster than you can invert the matrix, then it's faster and easier to use Cramer's rule. So in that sense, it's not useless.

On the other hand, if you're that hostile to abstract knowledge, then I suggest you re-read the first paragraph. Especially since you're not likely to need to solve systems of linear equations in any job you are qualified to hold.

[becomingagodo]

Basically, if you can take the determinant of a system faster than you can invert the matrix, then it's faster and easier to use Cramer's rule. So in that sense, it's not useless.
Okay, I can see why it is useful now.
On the other hand, if you're that hostile to abstract knowledge, then I suggest you re-read the first paragraph. Especially since you're not likely to need to solve systems of linear equations in any job you are qualified to hold.
I just like doing something one way, like how you can solve quadratic equation with the forumula or factoring it. It was annoying learning the quadratic equation, however if it has a use I will learn it.

On a side note, do you need to learn how to use a matrix before you can use the crammer's rule?

[drkitten]

On a side note, do you need to learn how to use a matrix before you can use the crammer's rule?

No, almost anything mathematical can be done by rote memorization. B.F. Skinner could probably have trained a pigeon to apply Cramer's rule.

But why bother?

The main reason that these things exist is because they help you understand the problem. But there are also a lot of cases in the real world where different specific problems can be solved more easily using different techniques.

For example:


I just like doing something one way, like how you can solve quadratic equation with the forumula or factoring it. It was annoying learning the quadratic equation, however if it has a use I will learn it.

Factoring a polynomial only works on a polynomial that has rational solutions; you can't factor x^2 + 3x + 1, for example, since the solution involves irrational numbers (specifically the square root of 5). The quadratic formula provides a solution in all cases -- but only works on polynomials of degree two. There is no known formula -- in fact, I think there's provably no closed-form solution -- to the general problem of a fifth degree polynomial, but factoring will work on any polynomial of whatever degree.

So if you need to work with polynomials, you usually need to know both methods. And you also usually need to understand enough about the methods to figure out which one you should use.

There's a reason I own both a screwdriver and a hammer.

[jimbob]

To me, every problem looks like a nail...