Linear Algebra Example: Span Questions

[@UnathiGX]

WOW! 3 years Later! Appreciate your come back!

[@elaine_chesoni]

This is amazing! Thank you so much for this video. I really appreciate how you emphasized the importance of stating what you're looking for (the preamble), what you're doing (the matrix you're writing and what it represents), and what the solution means (making sure you answer the question directly). Really really helpful. Thanks again!

[@shoremiayomikunoluwadaunsi1826]

Swears!

[@VictorNaftaly]

Saaaaaaaame 😢 especially when English is not your first language... even finding the question itself is a big issue

[@afailure805]

Just need a standard questions and a standard way to approach them and finally got you . Thank You .

[@angelm7309]

holy after so much searching this is the only playlist i need for lin alg

[@yizhang1302]

I really appreciate your videos! You are a great great teacher! I hope you can have more videos.

[@anujbhagat8151]

nicely explained. do not delete this video. may come back to this vid, if if i am ever in doubt , in future. thanks!

[@sankoktas420]

Dude is a legend

[@portillolopezjuanmanuel8079]

Awesome explanation! Although my ears hurt at that YES! in min 9:41 hahaha

[@scollyer.tuition]

When I learnt linear algebra (a long time ago...) we used to write an augmented matrix with a vertical line separating the last column from the rest. This distinguishes it visually from the matrix of vectors which you use in the second type of span problem.

[@lover-of-Shuhada]

We still use it in linear...

[@ObadaHakeem]

It's 3:55 am 😢

[@strangeworld4912]

4: 11 am 😢

[@Ashish-v1d8i]

Yes it is

[@joshuaigbeneghu4760]

5 am

[@dr.doctor8810]

12:05 am :{}

[@bossbabyy_00]

3.38 am 😢

[@lucci3319]

best ever span and its questions explanation. thankkk youuu so much sir! love from India! keep posting more lectures of David. c lay book. thanks againnnnn! :))))))

[@mosaif3590]

Sir I am from India ,this vdo is too helpful for us .❤❤❤❤

[@Maxd-c4v]

don't think anyone has clearly laid out why we are doing what we are doing as well as you. thank you. ;3

[@elbaavril9049]

Thank you for your explanation. I had doubts about span but now I understand it. Greetings from Peru

[@shoremiayomikunoluwadaunsi1826]

Good morning y'all. Thanks a lot sir! I have Linear Algebra exams this afternoon and this has really helped! Particular to the questions you solved and other versions in which the question may be written.

[@williamnguyen7622]

thank you sooooo much ... just even differentiating the 2 types of questions helps so much

[@himanshutiwari2601]

Great explanation dude❤

[@ravindrabind1504]

My question is related to Example-2: "Is u4 in Span{u1, u2, u3} ?" : Is same way of asking same question? Solution: [[1, 0, 5/2, 0], [0,1,-1/2, 0], [0, 0, 0, 1]] may considered as following: x1 + 5/2*x3 = 0 x2 - 1/2*x3 = 0 0*x1 + 0*x2 + 0*x3 = 1==> 0 = 1, because System has no solution, So we may tell that System is inconsistent

[@RaviPrakash-j4z]

In the 2nd example do we need to convert it into row echolon form or reduced row echolon form

[@ESHANHU-p3d]

Hi in which video do you talk about the Spanning column theory? You said it was in lecture video 9 but that video is labled as Matrix Equations and I did not find you mentioning the spanning column theory in that video. Thx!

[@HamblinMath]

webspace.ship.edu/jehamb/ela/lecture09.html

[@HamblinMath]

This part of the Lecture 9 video: kzbin.info/www/bejne/harUgJmYmqqbgpI

[@ESHANHU-p3d]

@@HamblinMath Thank you so much!

[@nadirbelkebir3]

Great video man ! Helped me a lot, wish me luck on my quiz !

[@xoppa09]

Very useful video. When you say row reduce the matrix , is it sufficient to be in 'echelon form' or does it have to be in 'reduced echelon form' which is the unique reduced matrix. also books seem to vary on echelon form, some require the pivots to be scaled to 1 while others do not require it.

[@adamjahani4494]

At 4:21 im so confused. Can we use a coeffient matrix instead of an augment matrix? Becuz I have that equal sign or vertical line between my 2nd and 3rd column. I can’t seem to get the row reduced echelon form unless I do a coeffient matrix without that line. I’m stupid idk what I’m doing. I’m learning this for a summer class and we are going way too fast. Linear algebra in a month feels impossible

[@HamblinMath]

No, because the question here relates to the specific vector b. I recommend watching the "span" lecture video for addition explanations: kzbin.info/www/bejne/p6m1l4mZf7qcnq8si=OtHWMIhJjQ5BSh92

[@Goal_baller]

Perfect

[@TECHNICALBEAST2020]

man really thank you lots of love from india

[@sumitbhale3645]

👍👍Sir explanation which clears all my doubts

[@tpsspace7397]

4 vectors cannot span R3

[@HamblinMath]

@@tpsspace7397 False

[@aan8474]

wonderfully explained!!

[@araizhaisanbek5912]

That’s really helped to understand! Thank you

[@AngelZangata]

You are such a good❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤ teacher

[@Hayat_kh202]

idk if i understood this right but when each row has a pivot it DOES span R^n/set of vectors but when a row is missing a pivot it doesn't span? or does it depend on what the question is asking

[@HamblinMath]

You need to be careful when using the word "it." If you have some vectors in R^n and you want to know whether they span R^n, construct a matrix with those vectors as its columns. If that matrix has a pivot in every row, then those vectors span R^n. If that matrix does not have a pivot in every row, then those vectors do not span R^n.

[@kusumrao5894]

its really amazing sir🥰🥰🥰

[@ahazizulhakimsumon1870]

Love your work man🤛

[@Rayyan-mo8gv]

Awesome video

[@mohammadk1]

Thank you habibi for helping me :)

[@mohammadsaad3037]

spanning column theorm? what are the rules for it other than the 2 shown in the video. I cant find it on google. All I keep seeing is the "Spanning Set Theorm"

[@HamblinMath]

The Spanning Columns Theorem (as I call it) states that the columns of an n x m matrix span R^n if and only if the matrix has a pivot in every row.

[@miksun_matematiikka]

Thank you, thank you and thank you one more time

[@miugirl24]

your videos are quite helpful but they would be even better if you took some extra time and went through row reducing the matrix in my opinion. thanks for ur effort !!!

[@HamblinMath]

You can find a full breakdown of the row-reduction process in this video: kzbin.info/www/bejne/bWPcpKitqb50ZsU

[@donmoore26762671]

Awesome instruction.

[@starliaghtsz8400]

i think you can say that {u1, u2, ......., un} spans Rn as long as no vectors are multiples of each other, it works for R2 and R3 and logic suggests it should keep working right?

[@HamblinMath]

Actually, it *doesn't* work in R3. Consider u1 = (1,0,0), u2 = (0,1,0), and u3 = (1,1,0). None of these vectors is a multiple of another, but they don't span R3.

[@starliaghtsz8400]

@@HamblinMath ooooh, yeah so that zero at the z coordinate means there is no pivot for the third row right?

[@starliaghtsz8400]

component*

[@HamblinMath]

@@starliaghtsz8400 Just think about it like this: With the example I gave above, the span of {u1, u2, u3} can't be all of R3 because it doesn't contain vectors like (1, 2, 3) that have a non-zero third entry.

[@starliaghtsz8400]

@@HamblinMath yeah thats what i was trying to say, ty

[@mikesgarage18]

An instance of linear independence in each dimension of R^3 implies a spanning set of vectors. Right?

[@HamblinMath]

I'm not sure I understand your question. If you have a set of three linearly independent vectors in R^3, then that set must span R^3. The reason has to do with the idea of "dimension," which you can learn more about in this lecture: kzbin.info/www/bejne/jnq9qZ-Eq6Z0oNE

[@عالممختلف-ذ6ظ]

teacher can you tell me how to transforme from augmented to row reduced i know the steps but when i try i didnt the result like you get it

[@mukhtarsuleman5291]

this helped a bunch, thanks alot

[@theojunming]

So for the set of vectors to span R3 it has to has a rank of 3 ? Correct me if im wrong tysm. Also, since each row is linearly independent of each other , can i say that they form a basis for R3 ?

[@mrjichoone6253]

yes

[@amar_1234_paul]

but in the scond question z the rank of augmented matrix and normal matrix is not same then how can we say that it spans?

[@micah2936]

Should I watch this after lecture 9?

[@irenebernardi3954]

Hi! do we know why sometimes the lecturer row reduces to simple echelon form, whereas sometimes all the way to reduced echelon form?

[@HamblinMath]

Some questions can be answered with just echelon form. When we're doing row-reduction by hand, it's less work for us to get to echelon form rather than the reduced echelon form.

[@irenebernardi3954]

@@HamblinMath ok makes sense! Also thank you very much for all of your content, this is the first time algebra makes sense to me and that's invaluable

[@chrisdalen1722]

Why does a pivot in the last collum mean no solution?

[@HamblinMath]

kzbin.info/www/bejne/oXXFc4d8q7aan8k

[@capybara-k6g]

for first example I thought it was in the span: 2V1 + V2 = b b is a combination of V1 and V2, therefor b is in span{V1V2}

[@HamblinMath]

It's not true that 2v_1 + v_2 = b. Check *all* the entries carefully!

[@capybara-k6g]

@@HamblinMath ah gotcha, thanks!

[@Joshua-rk7bl]

incredible

[@stopconfusions5370]

What’s a pivot

[@flidoofficial1848]

subscribed and here to stay

[@kodarkma7444]

The last column has a pivot, what does it mean sir????

[@HamblinMath]

kzbin.info/www/bejne/m4mvaaBua5qEm68

[@mrdawne5293]

The 2nd example doesn't make sense cause if we look at the last row . It's like saying 0x1+0x2+0x3=1 ?

[@HamblinMath]

Incorrect. The matrix being row-reduced is not an augmented matrix. You may want to watch this video to better understand the Spanning Columns Theorem: kzbin.info/www/bejne/harUgJmYmqqbgpIsi=t9Vt4rLewr9r6xnJ

[@denuwanvlog]

Perfect! ❤️

[@theojunming]

if i have multiple solution, can i still say that is b in span{v1.v2}?

[@HamblinMath]

If the equation x1 v1 + x2 v2 = b has one or more solutions, then b is in Span{v1, v2}. If there are multiple solutions, this just means that b can be "built" out of v1 and v2 in multiple ways.

[@vikasbansal4180]

Thank u sir for questions

[@drashysesodia512]

Thanks a lot sir .

[@Goal_baller]

3yr later, I am here

[@rajgurubhosale8680]

thanksss mannn

[@mrdawne5293]

Doesn't the 1st example have infinitely many solutions ?

[@ObadaHakeem]

@@HamblinMath why do we say it's many solution and not unique? We got values for x1 and x 2 and x3 and x4 doesn't exist cuz we have 3 columns

[@HamblinMath]

@@ObadaHakeem My previous comment was in error. The equation x_1 v_1 + x_2 v_2 = b has no solutions because the augmented matrix has a pivot in the last column. There is no "x_3" or "x_4" in this question; the vectors have 4 *entries* but that doesn't mean there are four variables.

[@lalisamanoban1126]

Thank u sm sir

[@garza8211]

Thanks :)

[@sarahkimani8063]

whats a pivot

[@thembzextreme090]

The first non zero In the row is 1

[@tannujangir5178]

Leading enrty in each column

[@makaka194]

subscribed*