How to Find the Rank of a Matrix (with echelon form) | Linear Algebra

[@WrathofMath]

Support this course by joining Wrath of Math to access exclusive and early linear algebra videos, original music, plus lecture notes at the premium tier! kzbin.info/door/yEKvaxi8mt9FMc62MHcliwjoin Linear Algebra course: kzbin.info/aero/PLztBpqftvzxWT5z53AxSqkSaWDhAeToDG Linear Algebra exercises: kzbin.info/aero/PLztBpqftvzxVmiiFW7KtPwBpnHNkTVeJc

[@nomyamar6103]

As someone struggling with university math, this was super helpful. Thank you so much.

[@WrathofMath]

Glad to help, thanks for watching!

[@RajnishKumar-cu2ww]

Hy p

[@MalekaShaukat]

Same me

[@Guppy_Flower]

why did you pick maths as a university major?

[@channelname9468]

@@Guppy_Flowerbro thinks you have to be a math major to have math classes 💀

[@kacpersambor6349]

finally someone who managed to clearly explain what to do, thanks a lot

[@WrathofMath]

Glad to help! Thanks for watching!

[@fireheart9715]

This was the simplest and clearest explanation I have ever heard of rank, no complicated concepts, no silly jumps from one matrix to another. Thank you so much for such a clear explanation :)

[@WrathofMath]

Thanks a lot - glad it helped!

[@Batooya]

I love how simple you made this explanation to be. My professor basically lectures like we've taken the course before and it's been kinda rough.

[@hristinamakedonska443]

omg i feel like you are talking about my professor

[@PuffyRippin]

Your videos are incredible. So well explained and to the point, thank you so much!!!

[@WrathofMath]

You're very welcome!

[@yondabigman4668]

quick, easy to understand, good job!

[@WrathofMath]

Thank you for watching!

[@alexminkin14]

2:25 how can you subtract row 2 from row 4 and get a zero in the first column and last row if you already changed row 2 by subtracting row 4 from it? This looks like a mistake. Correct me if I'm wrong, please.

[@pavels.1358]

Thanks a bunch 👍

[@acheacjun]

at 1:57 what did i miss, ist 2+3 = 5 and C3 ist 4 in its 2nd column ?

[@kartikeygupta3312]

At 1:57, 1+2=3; 2+3=5; 3+4=7; 4+5=9, so C3= C1+C2. If you still have some trouble with this, then I’m open to help you out

[@acheacjun]

@@kartikeygupta3312 i think at that time i was thinking about comparing each row instead of each columns, thx for correcting! ;)

[@archerdev]

Thank you so much for this great video. Math bless you man

[@rawansaleh-r9q]

thank you so much

[@001邱文典-o8w]

bro this is simple af ,thanks alot

[@WrathofMath]

Glad to help, thanks for watching!

[@janardannn]

lovely, had to take a detour to learn row echelon form and after coming back I saw the last example

[@DP-rq5nh]

Great video! I had a little trouble following the "row echelon form" examples though. Is this knowledge assumed or explained in a related video? Sorry if I missed it! Still one of the best "rank" videos I've come across!

[@DP-rq5nh]

nvm, found the related video lol "Finding Basis for the Row Space of a Matrix"

[@Deen9669]

This was super helpful. Thank you so much!

[@WrathofMath]

Glad it was helpful!

[@VElbo75]

How the heck did this explain take an entire class in college 🤯

[@mushtaqahamed9701]

Any jee aspirants?

[@ishaanchandel6966]

It's deleted for jee

[@ANONYMOUS-km8zs]

No only university students 😂

[@ParvejBiswas-qi4re]

Your 1 minute video is better than others 10 minutes video

[@benjaminasklivickas2357]

Thanks, man, great explanation!

[@WrathofMath]

Glad it was helpful!

[@VedantDarsan-pz1tn]

Thank you so much 😢 you have cleared the pain of my college math

[@WrathofMath]

Happy to help!

[@TechnoSoftlk]

You are a life saver❤

[@WrathofMath]

Thank you!

[@學習中的哈密瓜]

thanks for the video!!!

[@UmarRamzan-n9t]

Great thanks 😊

[@claytonhouser7578]

Very clear explanation compared ot msot channels and very short. Thans!!!

[@5050-Films]

Hi there, all of this is very well explained however in your final example, although you did get the correct rank, when you replaced R2=R2-R4 while simultaneously replacing R4=R4-R2 this was not a valid step - you replaced to linearly independent rows with what was (save for the sign) the same row vector. You will find that if you performed this in ANY matrix with any two rows say Rx=Rx-Ry and Ry=Ry-Rx the resulting new rows will always be Rx=-Ry when finished. As such this would generate a row of zeros by adding these new rows in your next row operation. As a result your matrix rank will go down. If you try this with a 3x3 matrix say ... R1=(2,3,4) R2 = (1,2,3) and R3=(1,6,2) and employ the strategy of R2=R2-R3 while simultaneously allowing R3 = R3-R2 then continue to REF you will say the Rank is 2, when in fact the Rank is 3 as the correct REF has 3 linearly independent rows (and columns).

[@fardaa3680]

thanks for great explanation

[@nihaarsatsangi2241]

Your content is always presented with such clarity, and I truly appreciate that!! Thanks a lot! Small verification required: We will calculate the row echelon form when rows and columns in the matrix are linearly independent, right? and then find its rank....... because we did not calculated row echelon form in case of linearly dependent rows and columns ie; matrix C and D

[@ParvejBiswas-qi4re]

Thanks a lot

[@zerodegreescelsius]

Spectacular!

[@WrathofMath]

Thank you!

[@BrushBurnerBRR]

this is so fkin easy and i hate my maths prof

[@bonniem1865]

Hot and smart, thank you kind sir!!!

[@Teo97b]

can you do ri rj and still get same rank?

[@WrathofMath]

Do you mean a row swap? Yes, a row swap will not change the dimension of the row space.

[@thihongngale7107]

The last example still confuses me, the third result in the E matrix, can I add row 4 to row 2 and then add row 2 to row 4 to eliminate them all ? After that I swap row 4 and row 2 so that the rank will equal to 2.

[@meshackmahindu5747]

Thanks alot

[@WrathofMath]

Glad to help - thanks for watching!

[@zahrayii]

Thanks so much for this helpful video 🥲

[@mohidahmed5874]

which app did you use

[@GEconomaster112]

thanks!!

[@WrathofMath]

You're welcome!

[@makingimpossible6096]

Super helpful. Thanks

[@WrathofMath]

Glad to hear it, thanks for watching!

[@mattshort5498]

I thought that that in row echelon form, all leading entries from the left need to be 1. This seems to contradict example A. Is what have I been told wrong?

[@WrathofMath]

Depends on the textbook/teacher. Some define row echelon to have leading 1s and some don't. I'm only beginning to get into the rhythm of my Linear Algebra playlist, and part of that is settling into the definitions we will use. I am primarily following the Anton text, and so we will define row echelon form to require leading 1s. My bad that this video is different. But again, both definitions are used, and I will generally be using the definition you cite. Thanks for watching!

[@1_in_8billion]

Thank you wrath

[@fieroh]

I think you mean linearly dependent right? Because doesn't linearly independent mean trivial solutions? which also means all the scalars are 0's?

[@WrathofMath]

Is there a particular timestamp you mean? The rank of a matrix is the dimension of the row space, and this is the number of linearly independent rows that the matrix has. For example the vector spans a line on the plane. The vector is not linearly independent of , and so it would not give us an additional dimension. However is linearly independent of . We cannot get by scaling , so the addition of into our set will give us an additional dimension. Said in matrix terms, the matrix [ 2 2 ] [1 2 ] has 2 leading 1s in its echelon form.

[@fieroh]

@@WrathofMath right sorry I was thinking that row on the matrix as a SLE and since the coefficients aren’t zero, they are linearly dependent. Very silly of me.

[@birojit1]

What notes app is that

[@channelname9468]

If there is x pivot columns in a matrix, does said matrix also have a rank of x?

[@Furkan-yv5ew]

Does swithcing from row operations to collumn operations change the result of the rank? Are we looking for row echelon form matrix that is equivaluent to the given matrix?

[@Alchemist70]

Regarding the 4th example, when I tried reducing to REF by carrying out operations on the rows as in other examples, I got rank(D)= 3. This contradicts what you got by carrying out an operation on the column. Please, I need clarification. Thanks in anticipation of your honorable response.

[@WrathofMath]

You'll have to review your work or try again. The rank is indeed 2. I just put matrix D into a RREF calculator and got 101 as row1, 011, as row 2, and all zeroes below that. Let me know how it goes and thanks for watching!

[@rameshbaburasineni1422]

@WrathofMath Thankful to you🥰

[@WrathofMath]

Thanks for watching!

[@Kenn-vd8ev]

Can simultaneous operations include the same rows? In the last example, where you took R2 - R4 and R4 - R2, when you take R2 - R4, there would be a new R2. However over here, you are taking R4 - old R2

[@arpanmukherjee8172]

Exactly, here he did it wrong. Thanks for addressing this

[@chinazaekperechinyere1252]

Are the dimension and the rank of a matrix the same?

[@WrathofMath]

No, the word dimension is typically used in the NxM sense for matrices, and I'm assuming you don't mean that. Instead you'd talk about the dimension of a vector space, which is certainly different from the rank of a matrix. However the rank of a matrix is the dimension of the column space of the matrix.

[@Fx_Explains]

How do you know the rank without using gaussian Elimination.

[@archerdev]

Stupid question, so if matrix A is known with 4 independent rows, and 2 independent column, the rank(A) will be 2? like min of rank-per-row and rank-of-col?

[@edechimebryan6381]

yep

[@jidrit999]

How to prove that row rank = column rank

[@ibrahim203]

I have so much confusion on row echelon form. UT matrix should be zeros okay got it. But what about diagonal ? Some say that all elements must be 1 and some say it doesn't matter :(

[@WrathofMath]

It can be confusing, I understand. It should be noted that the UT matrix is only required to be zeros for REDUCED row echelon form, not for general row echelon form. Regarding the leading entries, it depends on the text/author if they should be 1s or not. For many purposes, reducing the matrix to echelon form with leading coefficients of any sort allowed is sufficient, such as for determining the rank of a matrix - the reduction of leading entries to 1s isn't necessary. Presently I am basing my Linear Algebra playlist and videos off of the Anton text, which defines row echelon form in a way that requires the leading entries to be 1.

[@ibrahim203]

@@WrathofMath oh I get it now.. tyssm !! :)

[@إمبراطوريةالشيباني-و2ب]

Thanks 😊

[@WrathofMath]

No problem 😊

[@ashrafi9231]

you looked into my soul with eyes, sorry off topic ik 😂

[@WrathofMath]

When I look to the camera, 100% of my focus is on my words and speech, I have no RAM for the eyes!

[@syedmohammadabdullah]

shouldnt the rank be 3 for D and not 2?

[@WrathofMath]

No, because the third column is equal to the sum of the first two. There are only two linearly independent columns, and so the rank is 2.

[@mnqobimsizi4328]

WHY IS YOUR IPAD DRANING BETTRY LIFE LIKE THAT, TNX NOW I UNDERSTAND BUT YOOO

[@invisibleairxd261]

😂 I didn't notice that before. 82% - 71% in 3 mins

[@Nobel-y9e]

Is he teaching with ipad 9th gen or higher

[@WrathofMath]

I think I was using a 10th gen here, I don’t remember I’m using whatever the newest gen is now. Or at least what was the newest gen as of about a year ago.

[@PunmasterSTP]

The "rank" of this video is pretty high 👍

[@assassincover2358]

Am I supposed to focus with how handsome this guy is

[@Zay_2i]

From Iraq

[@akshargarg2718]

😄

[@simplexble3188]

dislike

[@arifakmalbahrom5522]

I don't undestand

[@WrathofMath]

Can I clarify anything for you?

[@ygermalsileshi8930]

are you crazy ?????????????

[@WrathofMath]

No, why?

[@channelname9468]

???

[@laodrofotic7713]

you dont understand ANYTHING OF WHAT YOU ARE TALKING ABOUT KZbinR.

[@phymadori545]

Thanks

[@WrathofMath]

No problem!