Fantastic tutorial! I was completely lost trying to solve systems of five linear equations, but your video illuminated the process. The way you used elimination method to systematically reduce the variables was brilliant. Your clear explanations and step-by-step approach were incredibly helpful. I really appreciate how you anticipated potential confusion and addressed common mistakes. This is going to be a huge help in my studies. Thanks for making this complex topic accessible! I'll definitely be recommending this to my classmates!
This video was a lifesaver! Solving systems with five variables always seemed impossible, but your explanation made it surprisingly manageable. I really appreciated the step-by-step approach using elimination. Let's say we have a simplified example: x + y = 3 x - y = 1 x + z = 4 y + z = 4 y - z = 0 Adding the first two equations, we get 2x = 4, so x = 2. Substituting x = 2 into the first equation gives y = 1. The last equation gives us y = z, so z = 1. Finally, substituting into the third and fourth equations confirms z=1. Your visual aids and clear explanations made this complex process much easier to understand. Thanks for breaking it down so effectively! I'm definitely going to rewatch this to solidify my understanding. Subscribed! This is far better than my textbook explanation. Thank you!
I would teach the more advanced students how to perform Gaussian Elimination with Complete Pivoting, (GECP) and they would be able to reliably solve any set of linear equations. This set of linear equations doesn't require GECP because they are linearly independent and already given in optimal order for direct forward elimination and back substitution. Teach the basics of linear algebra in 10th grade, the basics of matrix methods in 11th grade, and the basics of Gaussian Elimination, including GECP, in 12th grade. Gilbert Strang's "Linear Algebra" book would be ideal for teaching advanced high school students.
Think about this. Divide the first equation by 2 and subtract it from the last four equations. What happens? The unknown variable x disappears from the last four modified equations. Now scale the modified second equation and subtract it from the remaining three modified equations to cancel out the unknown y variable from the last three modified equations. Then scale the new modified third equation and subtract it from the remaining two modified equations to cancel out the unknown z variable. Then scale the new modified fourth equation and subtract it from the remaining modified equation to cancel out the unknown w variable. The final modified fifth equation contains only the unknown u variable. You have just performed forward elimination. Now solve for u, then for w, then for z, then for y, and finally for x, and you have just performed backward substitution. This is the most straight forward and simplest method, but could fail for many systems of linear equations. That is where Gilbert Strang's "Linear Algebra" book comes to the rescue to help students understand the Gaussian Forward Elimination and Back Substitution processes and why Gaussian Elimination with Complete Pivoting is the most reliable method for solving systems of linear equations.
Fantastic tutorial! I was completely lost trying to solve systems of five linear equations, but your video illuminated the process. The way you used elimination method to systematically reduce the variables was brilliant.
Your clear explanations and step-by-step approach were incredibly helpful. I really appreciate how you anticipated potential confusion and addressed common mistakes. This is going to be a huge help in my studies. Thanks for making this complex topic accessible! I'll definitely be recommending this to my classmates!
Lucky your students😊
Thanks 😊
hagoromo chalk, brains, and gains. This math teacher has it all.
Much appreciated, buddy 🙏❤️
Cool description of this Math Teacher 👍👍
chalk board, a challenging math question and a good teacher, NOSTALGIA
Good feelings 👍
This video was a lifesaver! Solving systems with five variables always seemed impossible, but your explanation made it surprisingly manageable. I really appreciated the step-by-step approach using elimination.
Let's say we have a simplified example:
x + y = 3
x - y = 1
x + z = 4
y + z = 4
y - z = 0
Adding the first two equations, we get 2x = 4, so x = 2. Substituting x = 2 into the first equation gives y = 1. The last equation gives us y = z, so z = 1. Finally, substituting into the third and fourth equations confirms z=1.
Your visual aids and clear explanations made this complex process much easier to understand. Thanks for breaking it down so effectively! I'm definitely going to rewatch this to solidify my understanding. Subscribed! This is far better than my textbook explanation. Thank you!
I would teach the more advanced students how to perform Gaussian Elimination with Complete Pivoting, (GECP) and they would be able to reliably solve any set of linear equations. This set of linear equations doesn't require GECP because they are linearly independent and already given in optimal order for direct forward elimination and back substitution. Teach the basics of linear algebra in 10th grade, the basics of matrix methods in 11th grade, and the basics of Gaussian Elimination, including GECP, in 12th grade. Gilbert Strang's "Linear Algebra" book would be ideal for teaching advanced high school students.
Perfect 👍
You brake the hard question down to the dimple steps well👍👍
Thank you 🙏
Nice video ❤❤❤❤❤❤
Thank you 🙏❤️
Nice question and comprehensive explanation 👍👍
Glad you found it helpful 👍
Do you know any different solutions?😊
Think about this. Divide the first equation by 2 and subtract it from the last four equations. What happens? The unknown variable x disappears from the last four modified equations. Now scale the modified second equation and subtract it from the remaining three modified equations to cancel out the unknown y variable from the last three modified equations. Then scale the new modified third equation and subtract it from the remaining two modified equations to cancel out the unknown z variable. Then scale the new modified fourth equation and subtract it from the remaining modified equation to cancel out the unknown w variable. The final modified fifth equation contains only the unknown u variable. You have just performed forward elimination. Now solve for u, then for w, then for z, then for y, and finally for x, and you have just performed backward substitution. This is the most straight forward and simplest method, but could fail for many systems of linear equations. That is where Gilbert Strang's "Linear Algebra" book comes to the rescue to help students understand the Gaussian Forward Elimination and Back Substitution processes and why Gaussian Elimination with Complete Pivoting is the most reliable method for solving systems of linear equations.
Nice 👍 👍👍
Can we solve this by using Matrices?
👍👍👍
😊😎
You're very handsome 😮
Oh,
you are too kind,Buddy ✋
You are too kind, buddy ✋
Informative video ❤❤
Thanks for watching 😊
I, personally, would use a row-echelon format (gaussian elimination) to simplify this problem.
Nice solution,
Do you know any different solutions for those students lower grade 10 which don’t know how to work with matrix?
What a beautiful question❤
Thanks
good question and simple solution
Thanks 🙏
you use just addition to solve this, very goood👌
Thank you! Cheers!
Please make videos of improving English skills too..
Thanks for the suggestion! 👍
@mathchemistryteacherMJ
I have been studying English and I need help
It’s my pleasure buddy
I’m sure your English Level is High, however you can teach me Math and during this we practice English 😊😊
@@mathchemistryteacherMJ
You are all heart ❤️