WOW! 3 years Later! Appreciate your come back!

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

Жыл бұрын

Swears!

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

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

It's 3:55 am 😢

@strangeworld4912

19 күн бұрын

4: 11 am 😢

Dude is a legend

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

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

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.

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! :))))))

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

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

Ай бұрын

We still use it in linear...

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

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

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

wonderfully explained!!

👍👍Sir explanation which clears all my doubts

Love your work man🤛

That’s really helped to understand! Thank you

Great explanation dude❤

Awesome instruction.

man really thank you lots of love from india

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

its really amazing sir🥰🥰🥰

this helped a bunch, thanks alot

Thank you habibi for helping me :)

Awesome video

incredible

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

2 жыл бұрын

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.

Perfect! ❤️

Thank you, thank you and thank you one more time

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

4 ай бұрын

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

@HamblinMath

4 ай бұрын

This part of the Lecture 9 video: kzread.info/dash/bejne/ga2lsciblajOfJM.html

@user-nx9sl8eq5c

4 ай бұрын

@@HamblinMath Thank you so much!

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

Жыл бұрын

yes

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?

Thanks a lot sir .

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

Thank u sir for questions

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

@HamblinMath

2 жыл бұрын

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: kzread.info/dash/bejne/in2O2s6HpqSnmtI.html

Perfect

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

Жыл бұрын

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.

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

2 жыл бұрын

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

2 жыл бұрын

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

@starliaghtsz8400

2 жыл бұрын

component*

@HamblinMath

2 жыл бұрын

@@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

2 жыл бұрын

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

Should I watch this after lecture 9?

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

17 күн бұрын

No, because the question here relates to the specific vector b. I recommend watching the "span" lecture video for addition explanations: kzread.info/dash/bejne/o6yGyLicerjPmLA.htmlsi=OtHWMIhJjQ5BSh92

Thank u sm sir

subscribed and here to stay

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

Жыл бұрын

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

@cherryang4644

Жыл бұрын

@@HamblinMath ah gotcha, thanks!

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

6 ай бұрын

You can find a full breakdown of the row-reduction process in this video: kzread.info/dash/bejne/aWat1dewpLynYMY.html

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

@HamblinMath

11 ай бұрын

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

11 ай бұрын

@@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

Thanks :)

3yr later, I am here

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

@HamblinMath

Жыл бұрын

kzread.info/dash/bejne/l4yAms9xZpi3lbA.html

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

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

@HamblinMath

Жыл бұрын

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.

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

@HamblinMath

9 ай бұрын

kzread.info/dash/bejne/nXiWpLZ_prTNmco.html

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

@HamblinMath

3 ай бұрын

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: kzread.info/dash/bejne/ga2lsciblajOfJM.htmlsi=t9Vt4rLewr9r6xnJ

subscribed*

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

@ObadaHakeem

2 ай бұрын

@@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

2 ай бұрын

@@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.

whats a pivot

@thembzextreme090

2 жыл бұрын

The first non zero In the row is 1

@tannujangir5178

2 жыл бұрын

Leading enrty in each column