Linear Algebra Example Problems - Spanning Vectors #2

[@TheLeo2030]

How isn't this the most popular channel on KZbin?

[@JO-ej3nh]

If my professor had explained it this way, I would have gotten it the first time. Thank you so much!!

[@AdamPanagos]

You're welcome, thanks for watching and for the kind words.

[@jan-willemreens9010]

...Rarely found such an unambiguous explanation on Spanning Vectors on the net by using just a simple example! Thank you, Jan-W

[@soomii5819]

HOW COME DID I NOT FIND THIS CHANNEL FROM THE BEGINNING OF MY COURSE. THANK YOU, YOU MADE IT UNDERSTANDABLE, SIMPLER AND EASIER. I HAVE A MIDTERM TOMORROW WISH ME LUCK

[@suleimanissack9509]

haha you are not alone, feeling the same. I have a final tomorrow

[@AdamPanagos]

Glad I could help, hope your midterm went well!

[@rayinoz]

Your 4m26s video is better than 2hour lecture. Thanks

[@AdamPanagos]

Thanks much, glad I could help! Best, Adam

[@GenuinePeacefulTimes]

Fantastic explanation! Thank you. This was just what I was looking for!

[@AdamPanagos]

Glad I could help, thanks for watching. Make sure to check out my website adampanagos.org for additional content (600+ videos) you might find helpful. Thanks, Adam

[@aridennis4415]

you lost a negative sign in there for V2.

[@serinacat4781]

very clear, I am your big fan

[@aibdraco01]

Thanks! U saved my GPA!

[@AdamPanagos]

Glad I could help!

[@DhanasekaranT-de4wz]

Run this video at 0.75x speed to catch up with the Professor. Great explanation of the concept though.

[@michchall843]

so clear! i honestly can't thank you enough

[@AdamPanagos]

You're welcome, thanks for watching. Make sure to check out my website adampanagos.org for lots of additional content that you might find helpful.

[@muhammadkumayl7761]

The real MVP

[@Megan-vi5uu]

this is so clear

[@AdamPanagos]

Thanks!

[@emmanuelmedina7147]

I like your videos! Which app are you using for make them? Thank you!

[@AdamPanagos]

I use an iPad app called Doceri (www.doceri.com) for most of my videos. This app lets you record all your handwriting ahead of time and use "breakpoints" to pause as needed. Once all the writing is down you can "play" the handwriting back while recording audio over it. I find this works much better than trying to write and talk at the same time. I'd definitely recommend checking out the app, I've found it very useful. Hope that helps!

[@Med_Alzubaidi]

شكراً ^_^

[@AdamPanagos]

You're welcome, thanks for watching!

[@ijuthomas7628]

I just with this can be downloaded 😂 bravo

[@tedbantone3]

Thanks

[@kabeloramodike]

Good day I'm a bit confused - why does the augmented matrix at 1:00 have two -2 values?

[@kabeloramodike]

OOOHH! Never mind - there was just a mistake when writing them in the previous line.

[@AdamPanagos]

Yes, that's correct. Sorry for the error. I want ahead and added an annotation to note/correct the mistake. Thanks!

[@peaceofheart5964]

Then it means only linearly independent vectors can span any vector space ?

[@AdamPanagos]

Not necessarily. You could have a large collection of dependent vectors that span a space. For instance, the vectors [1; 0], [0; 1], and [1; 1] span R2 since any vector in R2 can be written as a linear combination of these vectors. However, the vectors [1; 0] and [0; 1] also span R2 since again, any vector in R2 can be written as a linear combination of the vectors. In the first set of vectors, [1; 1] was clearly a linear combination of [1; 0] and [0; 1]. So, we had a set of dependent vectors that still spanned R2. In the second set of vectors, [1; 0] and [0; 1] are independent. We typically try to find an independent set of vectors to span a space since this will be the smallest set of vectors required. Hope that helps, Adam

[@peaceofheart5964]

@@AdamPanagos i got it ....... But tell me if we have to check for basis ...... We only need to see whether the vectors are L.I , no need to check for span.......right ?

[@AdamPanagos]

No, the definition of a basis is a set of linearly independent vectors that spans the space. So, you do need to check for both L.I. and span. As another example, the vectors [1; 0; 0] and [0; 1; 0] are LI in R3, but they don't span R3 so they aren't a basis for R3.

[@peaceofheart5964]

@@AdamPanagos can u plz give example of three L.I vectors in R3 which dont span R3

[@AdamPanagos]

That's not possible. If you have 3 linearly independent vectors in R3, then by definition they span R3. Hope that helps, Adam

[@happyplant8439]

what would happen if you solve the matrix and you get infinite solutions (like if X2 was a free variable)? would it span n-space or not? thanks:)

[@tszkinwong6170]

I guess it is a line in 2-d

[@reytorrera]

Where’s the sound?

[@zoem1294]

nice

[@AdamPanagos]

+Monica Xie Thanks!

[@ijazkhanniazi800]

Thanks

[@AdamPanagos]

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.

[@ElifArslan-l9g]

thanks