Solving Linear Systems Using Matrices

[@David-ob4sm]

KZbin has taught me more then any of my teachers. education system is broken hardcore.

[@GeoCalifornian]

+jeff bobson Everything wrong with education in America today can be found in government schools.

[@TheArnoldification]

+jeff bobson Your teachers in lecture probably want you to understand WHY this works, opposed to just showing you how to solve problems. If you're just solving problems without knowing what you're actually solving for or why the tricks you're using work, then you're really just following a cookie cutter recipe. You might learn less if professors decide to go more in-depth about the subject if the professor is confusing. Professors are responsible for giving you comprehensible lectures that cover all areas of the material you're supposed to cover, yes, but as a high school student (or college student) you also need to take initiative and responsibility to make the effort of mastering the material on your own. Of course there ARE bad teachers, but what this usually is is that students blame their teachers because they're personally lazy (which I am guilty of to an extent, actually).

[@David-ob4sm]

TheArnoldification yea it just sucks when he is always late and canceling classes. 20 mins late to the final. Also I prob would never use this.

[@TheArnoldification]

jeff bobson Oh, alright. That's completely different to what I was talking about. I've only had that happen to me a few times in high school, but never in college.

[@David-ob4sm]

lol your lucky. I had two classes this past semester that where like that and all my teachers where from foreign countries, which is fine, except when their accent is dam near gibberish. . Idk who hirers these people.

[@frywolf1817]

This video was a blessing from God. I was so freaking lost in class lol

[@_c3a3m_88]

Try with online school 😭

[@montpierce424]

Great video. I would add one more Elementary Row Operation: You can swap rows around in any order. For Example: In your first matrix, you could have moved Row 3 up to Row 1, then you'd already have a "1" in the first column of the first row. Thanks again for the great videos.

[@ceciliaappel7827]

Thank you so much for this! Your video is the only one I've found that explains this topic in a way I actually understand.

[@lauramatav]

Great tip on using only the second and third row to turn the third number in to a zero. This is where I kept getting stuck. Thank you for the video!

[@MandaNovokmet]

Wow! This video was very helpful.. thank you so much! You explained to me in 16 minutes what I had been trying to understand for over two hours.

[@shahzamanbelali8565]

Yeah same

[@AlRichards314]

Thanks for the comment. I appreciate hearing from people that find my videos useful.

[@jenniferflores154]

AlRichards314

[@steveyorke1230]

Can I get your WhatsApp number or email address pls

[@AlRichards314]

@@steveyorke1230 Hi. It's [e-mail]

[@squidward-04]

this helped me a lot....my professor is taking care of her child so she wasn't able to teach us this in class so I was struggling to finish my homework but now I followed along and was able to finish my homework, thank you so much!

[@AlRichards314]

Hey, glad my video helped. Cheers.

[@csbalu65]

I am so thankful to you, as my son has found your videos very informative and useful in his peparations. Keep up the good work. May God bless you.

[@RaRapidum]

Great Video ! Helped me out with my linear algebra course in college, Thanks alot !

[@LOGIGEEK]

i never understood what form we needed it to be in after so many videos you explained it very well and i have found the answer i was looking for

[@AlRichards314]

Happy to have helped.

[@hendrinakakondja2199]

Thank you very much.... This video really taught me a lot which i didnt understand from my lecture. Very helpful simple and easy to understand

[@elizabethhughes6312]

This really helped me understand just how matrices and linear systems work together. Thanks!

[@AlRichards314]

Hey, thanks for the comment. I'm glad it helped.

[@maryamashraf6370]

These videos are so helpful, thanks so much!

[@Driftwoodboy23]

Thank you for taking your time to help us students, I really appreciate it!!!

[@Akalankadilshan007]

Very helpful 💚 Thank you so much sir 💚

[@Shrawankumar91138]

Very helpful video Love from India 😊💐💐💐

[@emmanuelaboughe9149]

Very helpful. I got hundred !!!!

[@RanathCS]

thank u very much Sir.. very helpful.. easy to understand

[@bitsurfer0101]

That's great help. It helped to solve mesh analysis equations that I had (electronics).

[@humphreymubanga626]

the best explanation sir... I had so many problems with evaluation of 3x3 matrices using reduction (row operations).... #university of Zambia

[@alrichards1112]

Glad I could help. Have a good day.

[@humphreymubanga626]

+Al Richards blessed day sir God bless

[@ashwiniashu3813]

Thanks alot sir i have confusions after watching this video i get clear tq u sir

[@Mikey-mike]

Good one. Cramer's Rule is best, fastest, less mistakes, less time and paper. Also, always take the determinant of the matrix as the first step to determine if the system is independent or dependant. If the determinant is not zero, then the system is independent; and if the determinant is zero, then the system is dependant. An independent matrix has a unique solution. A dependent matrix has infinite solutions or is inconsistent.

[@monicaoyugi258]

very easy and simple to understand. Thanks!

[@studysmartderps7305]

Exactly what im looking for. The examples my professor went over weren't adding up correctly and i was doubting my algebra😅 and even his algebra

[@nickzecevic8214]

Thank You so much you dont understand how much I needed this

[@Varde1234]

You are coming in clutch for Engineering Math 1 students

[@marissahargan7521]

this is an amazing video! extremely helpful!

[@JK0097-u9lndkcn]

Thank u so much I understood very good 😘😘👏👏👏

[@jamessoften3811]

ib exam in 3 days and this helped me so much thank you kind sir.

[@rebellionmacky]

Question on your first sample the final row on the third matrix is 0 0 62 248. You substitute it to this equation 2x + y - z = 1 by multiplying the coefficients and constant. Your equation becomes 62z =248. What happen to the negative sign of z? The substitution looks like this right? 2(0) + (0) - 62z = 1(248)

[@bergen-schmidt]

Thank you so much! This was so helpful to follow along with!

[@MitchellHoldencmf]

Great video my friend. Extremely helpful.

[@tasnimhuka]

This video helped me alot thank you

[@KallMeChris]

I swear my problem is finding out what numbers are either subtracted or adding together with the rows to get zero or one, you seem to find it quickly when you stated that 2R1-3R1 I find it difficult to find what number to add or subtract its getting me frustrated I have a test thursday and Im not going to understand a thing about this section because of me not know what numbers to ad or subtract from it to get the corresponding zeros or ones, :(

[@AlRichards314]

The zeros are all about common multiples. Normally you work with a row that has a leading 1 to get zeros, but not always. For example if a leading number was 3 (in let's say row 2) and you wanted to turn a 4 below it (in row 3) to 0, then you would do 3R3 - 4R2 which would be 3X4 - 4X3 = 12 - 12 = 0.

[@omaramki]

you are the best man ... thanks

[@HausdorffLover]

Best video on this topic

[@Valphyr]

Thank you, was not aware of the restriction on the final zero row.

[@AnimeExtremeTX]

I will need to watch this another 10 or so times.

[@srutimandal2081]

you are a savior!!

[@AlRichards314]

Actually that's not what happened in the example. The first equation (originally) was 2x + y - z = 1 so row one was 2 1 -1 1. The third row (after 2 row operations) becomes 0 0 62 248 so it corresponds to the equation 62z = 248 and z = 4. The 62 is positive since it comes from the row operation 5R3 + 11R2 and so 5(-3) + (11)7) = -15 + 77 = 62 (not negative 62). There isn`t any substituting of row 3 into row one - that`s not a legitimate row operation. Hope this makes sense.

[@mathswithmohan7646]

Hi AIRichards, at min 11:58 of the video, wouldn't it be better to explain why there is infinitely many solutions? In one my of videos, I attributed the infinitely many solutions to the system having at least one non-leading variable.

[@AlRichards314]

Hi. Thanks for the comment. I agree that would be a useful thing to explain, but I don't think I'll rerecord the video just to add that comment. I might use a card there. Thanks for the suggestion.

[@mathswithmohan7646]

@@AlRichards314 Thank you for considering what I have just commented. Do you mind suscribing to my channel? I have uploaded a number of videos on systems of linear equations. You may want to take a look at it. Thank you.

[@AlRichards314]

@@mathswithmohan7646 Thanks. I see your channel is largely about linear algebra.

[@mathswithmohan7646]

@@AlRichards314 Yes, Mathematics is my focus niche. There are a lot of concepts pertaining to linear algebra. Vector and matrices are also closely related to linear algebra. I can see that your channel also focuses largely on calculus. Calculus is something that I will talk about it after I have covered all the concepts.

[@AlRichards314]

@@mathswithmohan7646 Actually Calculus is only a small part of my channel (probably 15% or less). Check out my new explanation regarding why the row of zeros implies an infinite number of solutions at kzbin.info/www/bejne/amiqeXebi7-ZrK8 .

[@VideoGameIdeas1]

Brilliant video, thank you very much for sharing it. : )

[@vade248721]

Helpful. Thanks

[@EltonNyabani]

THANKS

[@kismetbridgeforth9131]

Big help, thanks. Although I think the answer in Row 2, Column 2 should be -5 (negative 5), not 5, correct? Anyway thanks for showing us how to accomplish solving linear systems using matrices.

[@TrungTranimal]

No because he uses Row 2 subtracts Row 1 :)

[@andrewciuffreda7722]

incredibly helpful, thanks

[@shashimishra9073]

AWESOME VIDEO!!!!!!!!!!!!!!!!!!!!!!!

[@crashonthehumble]

Well done

[@musicoranime]

good teaching

[@biancaalvarez3680]

Do you have a video posted of when a coefficient is k?

[@AlRichards314]

Sorry, but I don't have a video that covers that scenario.

[@AsasAsas-mu1fg]

I really like the way that u explained , good job .

[@MrJoonasel]

Super duper video man ty!!!

[@fahimally3923]

thank you brother god bless you

[@pratikchakraborty3914]

Great help

[@samuelthomas1762]

you are really trying kudos

[@billywaters.as.billythekid8498]

real cool video your friend billy

[@bBbKce]

thks made me relate 3d geometry thks so much well understood

[@ZaidAlmymoni]

Realy you helped me thanks alot

[@salvadorgarcia5399]

Thank you very much sir

[@mangacartoonandsong4740]

Had coool video

[@S24KP6]

Thank you so very very very much!

[@VenyCharnita]

Thank you so much. God bless

[@sonarmen]

Dude. Thank you.

[@ethanstone2197]

Where did you pull 55 from

[@AlRichards314]

55 is the least common multiple of 5 and -11. I was using multiples of 5 to add to multiples of -11 to get 0. 5x11 = 55, then 55 + (-55) = 0.

[@chrisfrayre1271]

thank you very much

[@Ryan-tc5in]

Excellent video but isn't row 3 really row 1 by convention?

[@derkvaneggelen3292]

You’re amazing

[@AlRichards314]

Hey, thanks. Glad you found my video helped make sense of the math.

[@martaferreira1228]

Watching this I can point that the best approach is swap links, and if you work this way you can not do 2r1- 3r2

[@peterpaul4347]

Sir your style is hard to comprehend

[@AlRichards314]

Sorry to hear you feel that way. Was there something that needed some additional explaining?

[@Barbi32105]

thanks for the help !!

[@MrPJBarney]

Still learning from this video. Thank you. God bless. Jesus saves!

[@TheDestineyAngel]

Thank you so much.

[@haveanicetime]

Vielen Dank!

[@domadiusmichael3972]

Big Thanks

[@76454455555071]

this is the gaussian elimination method right?

[@AlRichards314]

That is correct.

[@fadzreenamyra7919]

thank you so much, idk why my teacher just read slide and don't tell us specifically like youtube videos

[@bassamal-jabri9121]

thank you so much

[@alialmarri659]

thank you MR for your help

[@meganfrey1663]

Thanks so much for the help!

[@arianarios9141]

Don't you have to subtract to move the variables in order

[@AlRichards314]

I'm not sure if I fully understand your question. However, you can also add using row operations to change certain positions to a 0, as long as you are adding opposites.

[@mercedesmalone973]

can you use this when you have like a larger matrix?

[@AlRichards314]

Mercedes Malone Yes you can use it on larger matrices. Sorry, I hadn't seen your comment until today.

[@vinayanand9554]

Thank you sir

[@mmumtaj8320]

Very easy method even i m very stupid to not this watching video as sooner.i m so plzd with myself

[@kudzaishecalvin8545]

thank you

[@abdelrahmankhatab4772]

thank you

[@na_trick_tutorial]

nice

[@thepenguintaco]

i tried following the way you did it, and the calculator gave me a completely different result for the matrix i had

[@shoun-kun6196]

JUSKO HIRAP AH

[@Love95056]

-5x-y+4=0 -8x-5y-1=0 the answer

[@ZaidAlmymoni]

can you please make more exinple abou t

[@AlRichards314]

+Zaid Almymoni Sorry, but I don't have any time to make new videos now.

[@ZaidAlmymoni]

+AlRichards314 ok thanks

[@4stoneblasters619]

i wonder how matrices are different from pure elimination.... I mean I can't see the difference

[@AlRichards314]

Matrices & row operations are just a different way of doing elimination. You are still adding or subtracting multiples of rows (instead of equations) to eliminate variables (leading ones).

[@princety2839]

2020 anyone? Currently in a pandemic and today is an Election Day( it went on for a long time)

[@As-if948]

I am still lost l don’t get the abreviations

[@AlRichards314]

Here's an example of the abbreviation. 2R2 - 3R1 means to multiply 2 times R2 and then subtract 3 times R1. When you see a subscript after an R it refers to a row. So 4R3 means 4 times row 3. Hope that helps.

[@As-if948]

@@AlRichards314 tha k you for taking te time to reply it means a lot

[@renekomanns7449]

is this not Gaussian method

[@AlRichards314]

Yes, you are correct. The is Gaussian Elimination.

[@frechjo]

O~O Ahhh, co... comic sans! I'm so triggered! jk, but there should be always a reminder that it's almost always a bad idea to use that awful font.

[@martaferreira1228]

This is not a very good technique we do tell the students not to do 2r1-3r3, it's not completly rigth, but placing 1 as the pivot or r1-3/2 r3.

[@Charlie43Leppo]

why can't you be my teacher

[@marvin7746]

there's a different matrix operation the basic one this is gauss not what I was looking for

[@AlRichards314]

This tutorial uses Gauss-Jordan elimination. Were you looking for one using Gaussian elimination?

[@aym_97]

How to put more than a like on this video ?

[@alrichards1112]

Put 2 likes ? LOL