I had completely forgotten about the gaussian elimination method and i remeber actually having a lot of fun doing it. I can't believe I forgot that. Thank's for the reminder.
When determinant is zero then you still can use Cramer's rule but you have to calculate rank of the matrix , use Kronecker-Cappelli theorem, choose submatrix with dimensions r x r where r = rank of the matrix such that determinant of this submatrix is nonzero Ignore equations which are not in the submatrix and unknowns which are not in the submatrix will be parameters
Hello sir! I just wanted to leave a comment to express my gratitude to you for making these videos. I’m currently a first year Computer Science student, however I’ve always had a love for math growing up, so I like trying to learn things about it in my spare time. Watching your videos has really made me slowly develop an enjoyment out of the topic of linear algebra (and greater degrees of math as a whole), and your words at the end of your videos regarding to never stop learning have helped me maintain motivation to continue my studies as a whole. Thank you so much for being willing to share the gift of learning with all of us; so many people take it for granted
My scool, and now even my uni, never required Gauss-Jordan method to be noted like a matrix, we would just continue from the original system of equations and switch to algebra to whenever it seemed convenient. I make a little curved arrow on the side pointing from one row to another and add some number p next to the arrow meaning you multiply the row from where the arrow starts with p and add it to the one you are pointing at. I think I used Cramers rule only once in my life because we had a massive system of equations with 4 or 5 variables and we only had to find the value of x
We had huge networks of systems we solved with this technique. It was what we called 'sparse' because many nodes only had a few connections. We had a computer program that would perform Gauss Jordan, but we optimized it for working with the sparseness of the matrix. As humans, we could see, "Well most of this row is already zeros...." but the tradeoff on a computer is spending time looking for such rows, or just go ahead and run through the steps (repeated solutions required under a second each). (matrixes of 40x40 up to as large as 90x90 were often solved this way)
Here's a trick I figured out for computerly pursuits. Suppose you have n data points; how do you figure out the polynomial that connects them? Let's say you have four data points. It goes like this: - Assume that you are trying to determine a polynomial equation y = Ax^3 + Bx^2 + Cx + D. Four data points means the terms will go up to x^3 and there are four coefficients total. - For each of your data points, plug in x and y to form an equation. For example, if one of your points is (1, 2), then you have the equation: 2 = A + B + C + D . And if another of your points is (2, 3), then you have another equation: 3 = 8A + 4B + 2C + D. Now do the same with your other two data points, and you'll have four equations. - Now you have a system of four equations, where your variables are A, B, C, and D. Solve for A, B, C, and D. Gaussian elimination will do; I'm a Cramer's rule sort of man myself. The point is, once you're done, you'll know what are the polynomial coefficients in Ax^3 + Bx^2 + Cx + D. There are of course other solutions that would require higher power terms. Like for example, if you have two points, the simplest polynomial would be of the form y = Ax + B, but we could also connect the points using any number of parabolas. This method assumes that the x^2, x^3, etc. terms will be 0, though in theory they could take on all kinds of values. There's just no way to say what those values would be from the data points given.
I find it much easier to do the elimination by hand. (a) + 4×(c) gives: 3y + 6z = 33 (d) (b) + (c) gives: 3y - z = 5 (e) (d) - (e) gives: 7z = 28, so z = 4 (f) (e) and (f) gives: 3y - 4 = 5, so y = 3 (g) (b), (f) and (g) gives: x + 6 - 8 = 0, so x = 2
Thank you! How I love mathematics! Pastor Richard Wurmbrandt said: The Bible is a mathematical book centered around the number 7. It has 7 dimensions: +,-,up,down,right,left and zero. Thank you for the beautiful Bible verses in the end.
Dear Professor, in the question, third equation - z coefficient is 2, but you have taken it into 1, and solved the equation…. Coefficient 1, is the matching equation for the arrived solution…. Dear Sir, please do the correction in the 3rd equation in the displaying question. Thanks and regards.
Is there a Cramer like rule for inverses? Elimination can be used where M*I = I*M^-1 but I don't know if there is an easier way; except using computers of course but where is the fun in that.
Even if you are just looking at larger matrices, using Gauss-Jordan is better. If I was looking to solve a setup using a 10 x 10 matrix, I'd look to use a computer. Failing that, I'd be using Gauss-Jordan.
Senpai, I can't see how to actually buy the t-shirt from the link. I was looking forward to buying it but had to wait till payday. Is it still available?
"Those who stop learning, stop living" - truer words have never been said
I had completely forgotten about the gaussian elimination method and i remeber actually having a lot of fun doing it. I can't believe I forgot that. Thank's for the reminder.
The little picture you click on to get to this video has the third equation as - x + y + 2z = 5
Thanks. I fixed it
Thumbnail
You made my maths strong like a rock.
I would love if maths becomes my distraction in my life i would like to have such kind of distraction in my life
Thank you for rewewing my old school days with me!
I love remembering this time.
I had so much fun with math.
When determinant is zero then you still can use Cramer's rule
but you have to calculate rank of the matrix , use Kronecker-Cappelli theorem,
choose submatrix with dimensions r x r where r = rank of the matrix
such that determinant of this submatrix is nonzero
Ignore equations which are not in the submatrix and unknowns which are not in the submatrix will be parameters
Now, I have to do a video on the Kronecker-Cappelli Theorem 😂
@@PrimeNewtons
😂😂😂
@@PrimeNewtons Do it.
Another great vid. Always good refreshers on things i do not use frequently but need from time to time.
Hello sir! I just wanted to leave a comment to express my gratitude to you for making these videos. I’m currently a first year Computer Science student, however I’ve always had a love for math growing up, so I like trying to learn things about it in my spare time. Watching your videos has really made me slowly develop an enjoyment out of the topic of linear algebra (and greater degrees of math as a whole), and your words at the end of your videos regarding to never stop learning have helped me maintain motivation to continue my studies as a whole. Thank you so much for being willing to share the gift of learning with all of us; so many people take it for granted
17:57 Come unto me, all ye that labour and are heavy laden, and I will give you rest.
Matthew 11/28.
My scool, and now even my uni, never required Gauss-Jordan method to be noted like a matrix, we would just continue from the original system of equations and switch to algebra to whenever it seemed convenient.
I make a little curved arrow on the side pointing from one row to another and add some number p next to the arrow meaning you multiply the row from where the arrow starts with p and add it to the one you are pointing at.
I think I used Cramers rule only once in my life because we had a massive system of equations with 4 or 5 variables and we only had to find the value of x
Greatest teacher of all times😊.. your videos helps me a lot sir thank you so much
We had huge networks of systems we solved with this technique. It was what we called 'sparse' because many nodes only had a few connections. We had a computer program that would perform Gauss Jordan, but we optimized it for working with the sparseness of the matrix. As humans, we could see, "Well most of this row is already zeros...." but the tradeoff on a computer is spending time looking for such rows, or just go ahead and run through the steps (repeated solutions required under a second each). (matrixes of 40x40 up to as large as 90x90 were often solved this way)
PLEASE MAKE VIDEO ON FINDING RANGE AND. DOMAIN OF FUNCTIONS🙏
Search my channel
Here's a trick I figured out for computerly pursuits. Suppose you have n data points; how do you figure out the polynomial that connects them? Let's say you have four data points. It goes like this:
- Assume that you are trying to determine a polynomial equation y = Ax^3 + Bx^2 + Cx + D. Four data points means the terms will go up to x^3 and there are four coefficients total.
- For each of your data points, plug in x and y to form an equation. For example, if one of your points is (1, 2), then you have the equation: 2 = A + B + C + D . And if another of your points is (2, 3), then you have another equation: 3 = 8A + 4B + 2C + D. Now do the same with your other two data points, and you'll have four equations.
- Now you have a system of four equations, where your variables are A, B, C, and D. Solve for A, B, C, and D. Gaussian elimination will do; I'm a Cramer's rule sort of man myself. The point is, once you're done, you'll know what are the polynomial coefficients in Ax^3 + Bx^2 + Cx + D.
There are of course other solutions that would require higher power terms. Like for example, if you have two points, the simplest polynomial would be of the form y = Ax + B, but we could also connect the points using any number of parabolas. This method assumes that the x^2, x^3, etc. terms will be 0, though in theory they could take on all kinds of values. There's just no way to say what those values would be from the data points given.
I find it much easier to do the elimination by hand.
(a) + 4×(c) gives: 3y + 6z = 33 (d)
(b) + (c) gives: 3y - z = 5 (e)
(d) - (e) gives: 7z = 28, so z = 4 (f)
(e) and (f) gives: 3y - 4 = 5, so y = 3 (g)
(b), (f) and (g) gives: x + 6 - 8 = 0, so x = 2
Thank you! How I love mathematics! Pastor Richard Wurmbrandt said: The Bible is a mathematical book centered around the number 7. It has 7 dimensions: +,-,up,down,right,left and zero. Thank you for the beautiful Bible verses in the end.
Wow, I learned something new today. I had a whiff of this way back before first year calculus but never saw it againn.
Dear Professor, in the question, third equation - z coefficient is 2, but you have taken it into 1, and solved the equation….
Coefficient 1, is the matching equation for the arrived solution….
Dear Sir, please do the correction in the 3rd equation in the displaying question.
Thanks and regards.
Yes, thanks
I still remember how to use Cramer's rule, it is simple and quick.
Sir, is it possible to explain to us that what the principles behind is ?
What a great video!
Please make a video on Gaussian integrals.
Currently we are studying matrices and determinants
We have studied gauss jordan elemination
I like both methods
Is there a Cramer like rule for inverses?
Elimination can be used where M*I = I*M^-1 but I don't know if there is an easier way; except using computers of course but where is the fun in that.
Such an amazing video 😊❤
Which country arr you from?
Nice! Polished.✨
I prefer inverting the matrix when possible. Easier that way.
Does this also work if we have a different number of equations with x, y, and z?
I like that, thank you man!!!
What mic do you use? Great videos btw 🔥
DJI MIC
Last 4 is easy - use last equation: -2+3+z=5 -> z=4
Even if you are just looking at larger matrices, using Gauss-Jordan is better. If I was looking to solve a setup using a 10 x 10 matrix, I'd look to use a computer. Failing that, I'd be using Gauss-Jordan.
Hello prime Network, can you please do for me this question
If 2^x = 3^y= 6^z, show that 1/x + 1/y + 1/z = 0
Senpai, I can't see how to actually buy the t-shirt from the link. I was looking forward to buying it but had to wait till payday. Is it still available?
It will be available again soon after everyone gives me feedback on the quality. Sorry about that.
this guy rocks
Professor I think the first method is called Martin's Rule and not Cramer's rule
Ohh I was wrong, I thought it was Martin's rule cause you used Matrix in first step.
Obi-Wan whispers: UUUUSE BAREISS.
Yikes!! ROFL!
Cramer is a German name, so not Craymer!
Your comment would be helpful if it included the correct pronunciation