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Linear Algebra Example Problems - Linear Combination of Vectors #2
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- čas přidán 7. 03. 2015
- adampanagos.org
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Given the vectors v1, v2, and v3, we see if the vector b can be written as a linear combination of the vectors.
This can be easily determined by constructing an augmented matrix, performing row operations, and finding the coefficients such that a1*v1 + a2*v2 + a3*v3 = b.
If values for a1, a2, and a3 can be found, then b is a linear combination of {v1,v2,v3} and we say that b is in the Span{v1,v2,v3}. If the augmented matrix has no solution, then b is NOT a linear combination of the vectors.
For this example, b CANNOT be written as a linear combination.
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This is the SHORTEST video that could give me the most HOLISTIC picture of linear combination and span!! Thank you!!
Thanks for the kind words, I’m glad you enjoyed the video! Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks much, Adam
@@AdamPanagos ooooh thanks for sharing. I will be a regular visitor!
Fantastic explanation, short and straight to the point! 😀
Thanks for the kind words, I’m glad you enjoyed the video! Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks much, Adam
I love you.
These videos are helping me not only to pass but to get A’s in my linear algebra exams and assignments!!! Thank you ❤❤❤
So glad to hear! Thanks for the kind words, I’m glad you enjoyed the video! Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks much, Adam
How to show that a vector of three components is a linear combination of two other three-components vectors?
Adam Panagos if Alpha 2=0 and alpha 1,3 are sum number after the reduce echelon form then what will be the solution linearly independent or dependent
Thanks جزاك الله خيرا ❤
You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam.
Thanks for making such videos, keep it up.
Thanks for the kind words, I’m glad you enjoyed the video! Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks much, Adam
Thanks, thanks, thanks. It's very clear!
+John Ortiz Ordoñez (InfZero) Excellent, glad it helped!
Adam
thank you
Sir is their any short trick for the purpose of competetive exams to get lc in 10-15 sec... Love u watch your videos.. Lots of love from India
Glad you liked the video and thanks for watching.
In general, I don't know that there's a short trick. The approach presented in the video is the best way to approach this type of problem in general (e.g. setting up a system of equations and seeing if there is a solution).
For a particular problem there might be a shortcut though. For example, if what if you're asked if [1; 2; 5] is a linear combination of the vectors [2; 0; 4] and [-1; 0; 7]? Right away you can see that it is not a linear combination because the 2nd element of vectors are both zero. There's no way to get the "2" that you need in the 2nd element of the given vector.
So, in certain cased you might be able to "see" the answer quickly, but in general, I think you have to use the approach from the video.
Hope that makes sense, best,
Adam
thanks very clear
You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam.
would you please be my professor?
you are really good :)
thank you very much
Thanks for watching!
Thanks!
You're very welcome, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam.
Good evening Adam, Don't get me wrong. I found your presentation clear, but what I do miss a bit is the geometric situation of the algebraic result, to show that vector b cannot be obtained from a linear combination of vectors X1, X2, and X3. Coincidentally I saw that X1=X3-X2, meaning that X1, X2, and X3 lie in the same plane within R3, so they are not linearly independent, and thus do not form a basis for R3. And apparently vector b does not lie in the plane spanned by (X1), X2, and X3. The conclusion is then that vector b cannot be a linear combination of (X1), X2, and X3. One final note, X1 can be considered redundant, hence the parentheses. I think this is the visualization of the algebraic result, or maybe not?! I'd like to understand what exactly happens given the result! (inconsistent system). Again Adam, this is not meant as a negative criticism of your video, but intended as a kind of supplement for a better understanding of the situation? I sometimes find Linear Algebra a bit confusing the way it is taught in general, and therefore not easy to study! best wishes and thanks, Jan-W
thanks a lot
what if there's infinately many solutions for alpha 3?
what if the last row is all 0's?, i know that means that x3 is a free variable. so would that mean that b will be a L.C of x1,x2,x3 ?
+Khoi Huynh Yes, that's correct. If we happened to get a last row that's all zero, then we know that x3 is a free variable like you said. So, this means we have an infinite number of ways that we could write the vector b as a linear combination of the three vectors. So, in this case b would definitely be a linear combination of the vectors. Hope that helps
Adam
Great explain
Thanks for the kind words, I’m glad you enjoyed the video! Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks much, Adam
what if infinite solution?
God bless u adam
Before I proceed F grammarly.Now thank you for thjis vid
Sir can u explain again using another problem???
What if I get in the final row 0=0? Will the vector still span?
Dick Justice Yes, you will have infinite solutions to combine them since x3 is a free variable
Is it mean it is linear independence??
Thank you so much !
+tsk1194 You're welcome, thanks for watching!
you helped me alot .. keep going and thank you
Nice explain
Thanks for the kind words! If you found the video useful make sure to check out my website (adampanagos.org) where I have a ton of other resources available and it's easier to watch my videos in a more organized fashion. Thanks, Adam.
how can we get the augmented matrix turn into the second one like [1010;0110;0001] , i dont know how to do this, plz help me or gimme a link to get a solution.. Thank you guys
Take a look at other videos earlier in the same playlist. The earlier videos go through the steps of performing row-reduction to manipulate a matrix into a different matrix. This video has an example:
czcams.com/video/YCyItKPDcSo/video.html
Hope that helps,
Adam
Bro I was confused at one part of the video u didn't explain how u got the answer
This video is one of many in the playlist. Earlier videos in the playlist worked numerous examples on augmented matrices and row reduction so maybe backtrack and watch those first. Also, might be easier to watch everything in sequence on my website www.adampanagos.org/ala. Hope that helps, Adam
very helpful, thank you a lot, peace v
You're welcome, thanks for watching!
The thing i want to understand you didint explain, how did change numbers to 0
That's just the standard "row reduction" process. I didn't do the steps in this video, but I have several videos earlier in this same playlist of videos that show you how to perform row reduction. Take a look.....
αστα αυτα τωρα, καμια μπυρα πινεις;
thank you
thanks a lot
You're welcome, thanks for watching!