The elemental ideas of span, linear mixtures, linear dependence, and bases.
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I think this explanation helps me remember the meaning of linear dependency/independency for good
you literaly made me fall in love with maths once again
You are true hero
Amazing job
Dev1ce ass
thank you Sir
Hi,
If Cartesian Coordinate System gives just scalar multiplication to basis vector (i, j).
What are polar coordinates doing… In which one in just scalar distance(r) and the other angle is?..
Which type of tensor is angle in the set of (distance, angle, area volume).
Could you make sense of this….
Thank you for the content it makes it easy to understand Gilbert Strang lec in (visually)
I want to buy a book to read more about linear algebra along side these videos and also solve problems for practices. What would be a good book to purchase. I don't want it to be a typical thick textbook though. Any recommendations?
9:30 If the set of vectors span the full space , they will be linearly independent ! Or for linearly independent their x and y components must not collapse?
i like your voice
Whoever invented the 2x play speed when tap-holding on YouTube videos deserves a noble prize
شكرا Thanks
my timestamp 6:15
What All Should I already know to learn this? I am in 10th grade(ready for 11th)
2:11 where I lost it..
Amazing, youre are very very good, congrats.
I wish I had this lecture at high school. So clearly explained.
Yes I have got that defintiion, And for a nD dimensional System There could be only n Independent basis vectors When there is one more than this, This will be a linear combination of some of those independent basis vectors. Cool
you're a lifesaver! thanks for feeding my curiosity!!!
You explained it with great clarity. Thank you.
I love your videos ❤
A plane is an infinite collection of vectors that satisfy the plane. Change my mind.
Beautifully explained!
100% intuition
The visuals are so purposefully made and so very helpful to visualize for these concepts. Otherwise, something like "linear independence" meant nothing more than some more math. Thanks a lot!
Please what’s the correct answer if the quiz
Thank u ! I am a freshman majoring in mathematics , I had trouble learning linear algebra.These videos have inspired me a lot.
thank you for making these videos!
Are you the guy from Khan Academy?
As a foreign student, is it really "deee pendent"?
8:42 any one of the vectors can be expressed as a linear combo of the other two, right?
8:15
the span of two vectors in a 3d space is a plane
3:17!