Hi! not necessarily, for example if you had these two vectors: (1,3,5,7) and (2,6,10,14), you can see they are not linearly independant as the second one is clearly two times the first one. pd:I know it's been 8 months, so you probably don't need the answer anymore, but other people may.
question: according to the last example, is the opposite also guaranteed? If we have more entries in each vector than the number of total vectors, does that make it linearly independent?
No only if every column has a pivot. Pets say that you have a set of 2 vectors with 3 entries. If the two vectors are multiples (which is the same as overlapping) the set would be lineary dependent
@@monsieurLDN Lol check the newest comment, I literally asked the exact same question and then read one comment down and you answered my question. Thanks!
What if there are more variables in the vectors than the matrix has columns? For example vectors v_1 = (1,2,3) and vector v_2 (2,3,4) would come out (just play along) and have one free variable but that would still mean they have two "stable" variables? Which technically would be enough to form a plane? Or would it still shrink in size and form a line, since that would still mean there is a solution other than 0 for the coefficients c_1*v_1+c_2*v_2=0-vector.
your comment about the theorem that states if a set contains the zero vector makes it linearly independent is incorrect - it's the other way around because if one of the vectors were zero then we would have a dependence relation
![Midterm 1 True False Easy/Medium/Hard [Passing Linear Algebra]](http://i.ytimg.com/vi/LR2LJLq6gpo/mqdefault.jpg)
![Midterm 1 True False Easy/Medium/Hard [Passing Linear Algebra]](/img/tr.png)
![Rank & Nullity; How to Find a Basis for Null Space and Column Space [Passing Linear Algebra]](http://i.ytimg.com/vi/jJK_6pO1evo/mqdefault.jpg)
4 years later and you're still helping people... ur a legend, thanks man!
I can tell the guy who does these is handsome.
love u graham
Focus
My boy thirsting in linear algebra comments section. Y'all wild.
Lol you were right 😏
Trueeee
i love how the voice cracking got more and more intense as the video went on, great vid btw :)
it's probably cause he's so passionate about math
thought I was the only one lmfao
We just learned about linear dependence this week and your explanations make it easier to understand :-)
Very good video. You don’t explain it using annoying theorem lingo. Quick and easy ways to check a span. Thanks!
2:00 man after so many vids you're the only one who answered my question thanks sm
I watched this video the night before my first linear algebra exam and now I'm watching it again the night before my linear algebra final lol
I watched this video when I was 5 years old. Now I won the Nobel prize in math.
@@michael654 whattttttttttt
@@rohhanbhardwaj true story, i was the nobel prize
Ur the goat bro, clean simple explanation n it rlly makes sense
Archer's teaching Linear Algebra now
THANK YOU. Very helpful and easy to understand
didn't understand linear indepdence until i watched this video. thanks!
This really breaks it down, thanks!
or u can find the determinant and see that it equals zero so its linear dependent.
My go to method
only works in square matrices, so this is a most general method presented in the video.
Your definition at the beginning of the video was very good, most other sources make it way too complicated.
thank you so much! i love how straightforward this was!
You’re the GOAT
THANK YOU YOU ARE A LIFE SAVER
Really appreciate the videos, can't thank you enough 🙏🙏
Thanks brofessor!
what if there are more elements in each vector than vectors (ex. a 4x3 matrix) would that also mean it is automatically linearly dependent?
Hi! not necessarily, for example if you had these two vectors: (1,3,5,7) and (2,6,10,14), you can see they are not linearly independant as the second one is clearly two times the first one.
pd:I know it's been 8 months, so you probably don't need the answer anymore, but other people may.
@@Lucas-yh5zz its after 1year helps me . thanks
Thank you
can you not do two vectors cross together then dot with the third verctor and if it equals 0 than linearly dependent?
Thank you so much!
Thnx man ;)
nah jit was goin thru puberty in this video 😭 jokes aside thx for the great explanation!
question: according to the last example, is the opposite also guaranteed? If we have more entries in each vector than the number of total vectors, does that make it linearly independent?
No only if every column has a pivot.
Pets say that you have a set of 2 vectors with 3 entries. If the two vectors are multiples (which is the same as overlapping) the set would be lineary dependent
@@monsieurLDN Lol check the newest comment, I literally asked the exact same question and then read one comment down and you answered my question. Thanks!
What if there are more variables in the vectors than the matrix has columns?
For example vectors v_1 = (1,2,3) and vector v_2 (2,3,4) would come out (just play along) and have one free variable but that would still mean they have two "stable" variables? Which technically would be enough to form a plane? Or would it still shrink in size and form a line, since that would still mean there is a solution other than 0 for the coefficients c_1*v_1+c_2*v_2=0-vector.
Nvm literally the last comment responded to this.
GOAT
The description about the zero vector is wrong according to my homework
You are going to help me pass my Exam >> XD
great stuff
5:54 nice
9:00
@@chrisdeluisa6648 6:09
king
your comment about the theorem that states if a set contains the zero vector makes it linearly independent is incorrect - it's the other way around because if one of the vectors were zero then we would have a dependence relation
Doesn't it depend? you can only use the trivial solution of 0 to represent a 0-vector
Nvm
1:54 wtf is that supposed to mean
hoca aldin bizi sirtina gidiyoruz
having only a trivial solution defines linear independence. you said we don't want that at the 3:00 mark. lmao you are wrong
I don't really grasp how you know what you're doing to row by using c1, c2, and c3.
He's solving for the pivots variables in each row by using the columns in that row
Okay so why did my professor make it so complicated for no reason
can you show us how you went about the row reduction, am kinda getting some weird values
mee to
buddy, explain it to me like u would explain it to a 7 year old.
Are you teaching those who are Learning it for the first time or are you lecturing a pro😒.
Phattest gg's
some people know how to teach some don't and this guy does not.
honestly it made a lot of sense
I thought he did a good job. Maybe we should look at ourselves before commenting on the qualities of others.