Cramer's Rule / Mathematical Derivation / I'M DESPERATE

[maddystyles]

Heyy

I'm in senior year of highschool (not in the US tho, so the system is a little different I guess) and have to make a presentation about the topic "Cramer's Rule - mathematical derivation and application". I already know how to apply it but what I don't understand at all is the derivation. I've searched the entire internet in my first language and then switched to English in hope to find more, but still didn't really find anything, only "Proofs" but no derivation. I only found like 2 derivation examples that were completely difficult and included other math topics that I never had in school yet.

Another thing I didn't really understand is when it is used, as to determine the solutions of a linear equation system is mostly easier with the Gaussian rule.
I'm really desperate and hope someone here can help me

Thanks


Also I'm sorry if this is in the wrong category, idrk where it belongs to

 

[tkhunny]

To your last objection, Cramer's Rule for the solution of linear systems is more of an existence idea than a practical application. Having said that, as always, do not discard things that you know because something else seems easier at the moment. You said, "... mostly easier with the Gaussian rule." So? Keep an open mind and understand all that you can understand. I cannot imagine deliberately avoiding useful information because you do not see the purpose today. There is a reason why it is taught. It contains additional insight that does not exist elsewhere.

My views. I welcome others'.

 

[pka]

Heyy

I'm in senior year of highschool (not in the US tho, so the system is a little different I guess) and have to make a presentation about the topic "Cramer's Rule - mathematical derivation and application". I already know how to apply it but what I don't understand at all is the derivation. I've searched the entire internet in my first language and then switched to English in hope to find more, but still didn't really find anything, only "Proofs" but no derivation. I only found like 2 derivation examples that were completely difficult and included other math topics that I never had in school yet.

Another thing I didn't really understand is when it is used, as to determine the solutions of a linear equation system is mostly easier with the Gaussian rule.
I'm really desperate and hope someone here can help me

Thanks


Also I'm sorry if this is in the wrong category, idrk where it belongs to

HERE is detailed page on Cramer's Rule.

 

[Dr.Peterson]

What is the difference in your mind between a proof and a derivation?

If a "derivation" has to be a way in which one might discover it without already having it in mind, solving a 2-variable system symbolically provides a strong motivation for the idea, which one might then generalize and attempt to prove in general. That might be sufficient for your purposes.

A general proof, for all n, is likely to require either relatively advanced notation or concepts, just to keep track of everything! But starting with a simple case can make all that easier to follow. If the Wikipedia proof(s) are beyond you, perhaps you can tell us what knowledge you do have, and where the proof you are interested in exceeds that, so we could help interpret it for you.

 

[Steven G]

Can you please explain what you think the difference between derivation and proof is. That will surely help us answer your question.

Here is what I would do to prove cramer's rule for a 2 equation - 2 variable situation. You will be able to show this easily!

Start with with 2 equations:
ax+by=c and dx+ey=f
Solve this for x and y using any method you know (but not cramer's rule!). Note when there is no solutions as well.

Now solve for x and y using cramer's rule. You will get the exact same results as above. This will show that cramer's rules is valid in this situation.

Since the proof for more equations/more variables is above you, then this is the best you can do.

Good luck with your presentation!