Thanks so much for this. Really intuitive explanation of both the theorem and its corollaries. I would not have understood it so thoroughly if it weren't for this video!
I have a question, in 5:50, you mentioned that a set that spans R3 doesn't have to be linearly independent. But aren't the two statements mathematically the same? A set of 3 linearly independent vectors must span R3, also a set of 3 vectors which span R3 has to be linearly independent, therefore the statements are iff to each other. Can someone help me about this?
@@ryanorshine I think I understand now, if there are more than or equal to 4 3d vectors, they are definitely not linearly independent, but they could span R3. Thanks!
Thanks so much for this. Really intuitive explanation of both the theorem and its corollaries. I would not have understood it so thoroughly if it weren't for this video!
Thank you!!!
I really love your videos! They are so well spoken, and it really helps with understanding abstract concepts. Thank you!
Thanks so much!!
Love the video and his ENERGY!!!
This helped a lot amazing work
I have a question, in 5:50, you mentioned that a set that spans R3 doesn't have to be linearly independent.
But aren't the two statements mathematically the same?
A set of 3 linearly independent vectors must span R3,
also a set of 3 vectors which span R3 has to be linearly independent,
therefore the statements are iff to each other.
Can someone help me about this?
What if you added another vector in R3 to a basis of R3? It must still span R3, but now the four vectors are linearly dependent.
@@ryanorshine
I think I understand now, if there are more than or equal to 4 3d vectors, they are definitely not linearly independent, but they could span R3.
Thanks!
thank you for your work and kindness - from old student😊
Awwww thank you so much!!! When did I teach you? 😊
you're so happy it makes me happy too, thank you so much !
you are a god amongst men, thank you so much
So GEN X Dr. Frankensteins requires 10 linearly independent Victors?
this video was magnificent
Thank you!!!
where can I watch oall the proofs about linear algebra ? I like your teaching style I just start to read the book. thank you~~
It’s on my playlists :)
that is a good question...Could you gvie the link ?The only thing I find is the course not the PROOF.Thank you again. @@drpeyam
Thx for this video! This helps me a lot! And you are very good at explaining and summarizing!
Based on the thumbnail..I thought this had something to do with combinatorics
steinitz?
thank you
wow 31 minutes let's gooo!
Thanks.
1:56 Generates/spawns ℝ³
You will not replace us!!
How can you prove that "gen" spans R^3?
It’s the definition of Gen, gen means spans
@@drpeyam oh yes thank you! I was actually referring to that beginning subset {(8, -12, 20), (7, 2, 0), (0, 2, -1)}
There’s a video on that somewhere, but you row reduce and count the pivots
Watching...
I thought this said “replacement theory” and was confused 😂😂
What’s replacement theory? Haha
Fringe political stuff, hence my confusion
Oh! lol
First!