I have searched so hard for an explanation like this. Instant subscription, I can see you will be helping me a lot in the future.

@GlassofNumbers

3 жыл бұрын

Thank you so much! I was looking back at the video nd had been wondering if it's too long. I should really make one with a focus on the trick so that it's more convenient to everyone! 😁

@tacticalmistress

3 жыл бұрын

@@GlassofNumbers Sure, I hear you. But this example is great, because the trick is used again and again to avoid fractions that keep wanting to come up throughout all of the operations. It really is insightful to realise that this is a trick that can be used from the beginning until the end.

@GlassofNumbers

3 жыл бұрын

That's a good point! So it is indeed good to show how we use the trick again and again to avoid fractions. It doesn't always work (when one pivot is a multiple of another). This trick comes from a theorem from number theory, but I completely forgot the name of it. (Too long ago)

@tacticalmistress

3 жыл бұрын

@@GlassofNumbers Cool! Maybe make a video on that, and pointing out when and when not this trick will work relating to the pivots.

This is amazing! My teacher showed us this method but it is really hard to practice since i can't find a textbook that uses it and i can't understand my notes at all at this point lol If You know the name of any textbooks with examples and solved exercises that uses this method ID appreciate if You share it! Thanks!

@GlassofNumbers

Жыл бұрын

Do you mean Gaussian Elimination or the trick to avoid fractions?

@celephaishyde9423

Жыл бұрын

@@GlassofNumbers trick to avoid fractions. We are currently going through gaussian elimination but my teacher is on a mission to avoid fractions like the plague , so i guess the next subjects Will be the same way.

YAY thank you

@GlassofNumbers

9 ай бұрын

Thank you for the comment! Please help me by sharing the video 😁👍

Nice!

@GlassofNumbers

3 жыл бұрын

Thank you for your comment!

sooo good

@GlassofNumbers

2 жыл бұрын

Thank you! Please help me share my videos 😁

Hi, are we allowed to multiply both rows before addition? That is, are we allowed to do 5R2-7R1 in a single step? We can then continue until we get a diagonal matrix, and only deal with fractions at the end.

@GlassofNumbers

2 жыл бұрын

It will work, but that step will not be an elementary row operation anymore. If you are taking a class to learn this, make sure to ask your teacher whether he or she wants to see each step as elementary row operations 😁

@OpenLessonsMy

2 жыл бұрын

@@GlassofNumbers So the question really is, why is the 3rd ERO defined so specifically as multiplication of one row added to another? Rather than saying that there is 3 we can do, i) exchanging rows ii) multiplying row with scalar iii) Addition of rows AND any combination of the above. Is it merely convention or some real reason behind it?

@GlassofNumbers

2 жыл бұрын

@@OpenLessonsMy Actually, we are doing combinations of the three elementary row operations, when it comes to, say solving a system. Maybe we can get the calculation done more quickly by doing 5R2-7R1. There are reasons for why we stick to those three row operations (math.stackexchange.com/questions/172653/what-makes-elementary-row-operations-special?noredirect=1&lq=1) Also, it's good to mention that each of the three row operations can be represented by left multiplication of an elementary matrix.