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!
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! :))))))
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.
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.
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.
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
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.
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 ?
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!
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: ua-cam.com/video/XIZxlNvAAjo/v-deo.html
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"
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
No, because the question here relates to the specific vector b. I recommend watching the "span" lecture video for addition explanations: ua-cam.com/video/qxRfVcJUihM/v-deo.htmlsi=OtHWMIhJjQ5BSh92
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.
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?
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 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.
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.
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 !!!
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
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: ua-cam.com/video/OyqOfbeEhL0/v-deo.htmlsi=t9Vt4rLewr9r6xnJ
@@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.
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!
Swears!
Just need a standard questions and a standard way to approach them and finally got you .
Thank You .
I really appreciate your videos! You are a great great teacher! I hope you can have more videos.
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!
It's 3:55 am 😢
4: 11 am 😢
Yes it is
5 am
thank you sooooo much ... just even differentiating the 2 types of questions helps so much
Awesome explanation! Although my ears hurt at that YES! in min 9:41 hahaha
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! :))))))
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.
We still use it in linear...
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.
Thank you for your explanation. I had doubts about span but now I understand it. Greetings from Peru
wonderfully explained!!
Great video man ! Helped me a lot, wish me luck on my quiz !
👍👍Sir explanation which clears all my doubts
That’s really helped to understand! Thank you
Awesome instruction.
Great explanation dude❤
Love your work man🤛
this helped a bunch, thanks alot
its really amazing 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
man really thank you lots of love from india
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?
Sir I am from India ,this vdo is too helpful for us .❤❤❤❤
Thank you habibi for helping me :)
incredible
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.
Awesome video
Thank you, thank you and thank you one more time
Thank u sir for questions
Thanks a lot sir .
Perfect! ❤️
Perfect
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
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.
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 ?
yes
Thank u sm sir
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!
webspace.ship.edu/jehamb/ela/lecture09.html
This part of the Lecture 9 video: ua-cam.com/video/OyqOfbeEhL0/v-deo.html
@@HamblinMath Thank you so much!
An instance of linear independence in each dimension of R^3 implies a spanning set of vectors. Right?
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: ua-cam.com/video/XIZxlNvAAjo/v-deo.html
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"
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.
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
No, because the question here relates to the specific vector b. I recommend watching the "span" lecture video for addition explanations: ua-cam.com/video/qxRfVcJUihM/v-deo.htmlsi=OtHWMIhJjQ5BSh92
subscribed and here to stay
You are such a good❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤ teacher
if i have multiple solution, can i still say that is b in span{v1.v2}?
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.
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?
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.
@@HamblinMath ooooh, yeah so that zero at the z coordinate means there is no pivot for the third row right?
component*
@@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.
@@HamblinMath yeah thats what i was trying to say, ty
Should I watch this after lecture 9?
Hi! do we know why sometimes the lecturer row reduces to simple echelon form, whereas sometimes all the way to reduced echelon form?
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.
@@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 :)
The last column has a pivot, what does it mean sir????
ua-cam.com/video/eXL8m865QeM/v-deo.html
Why does a pivot in the last collum mean no solution?
ua-cam.com/video/kDbBTFvQgig/v-deo.html
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 !!!
You can find a full breakdown of the row-reduction process in this video: ua-cam.com/video/72ysuwtYA0c/v-deo.html
3yr later, I am here
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}
It's not true that 2v_1 + v_2 = b. Check *all* the entries carefully!
@@HamblinMath ah gotcha, thanks!
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
subscribed*
The 2nd example doesn't make sense cause if we look at the last row . It's like saying 0x1+0x2+0x3=1 ?
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: ua-cam.com/video/OyqOfbeEhL0/v-deo.htmlsi=t9Vt4rLewr9r6xnJ
Doesn't the 1st example have infinitely many solutions ?
@@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
@@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
The first non zero In the row is 1
Leading enrty in each column