Linear Algebra 2k1: Examples of Linear Combinations

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you really have the best linear algebra videos and course I can find on the internet. Thank you so much. More people need to know about you

theflaggeddragon

I do guess on the question " does any linear combination between two vectors of the form [ x y 0 ] gives another vector [x' y' 0] ? ". I believe this is true, because a linear combination involves a multiplication with a scalar (and 0 is the null element for the multiplication) and a summation (well, 0 is the neutral element for the sum), so the result will be always zero. This can also be used to prove the fact that the span of two vectors in R^2 is the entire plane, but no other point outside that plane. I also think that this can generalized to the vectors [x y z 0], which span the space in R^3 and so on by induction. The same property doesn't hold for the vectors of the form [x y c] with c != 0; because the linear combination will eventually change that "c".

diaryofanb

1:10 : Main Example : 2a - 3b (a, b are vectors)
1:20 : Geometry Vectors
1:40 / 3:56 : IMPORTANT: no coordinate system in this example!! Pure geometric considerations
4:15 : Polynomials+ IMPORTANT: note how different are wrt geometric vectors!!
6:43 : Rn

antonellomascarello

In case of polynomials, whatif they dont have any common property. Is it so that still there will be some other property except the root case that will be preserved?

amarparajuli

for the sake of curiosity, why are you against the use of coordinates for geometric vectors?

AndresLara-hyip

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... No! ... I can't! ... I can't take anymore! I tap out!

Looks like I wasn't up to the Linear Combination Challenge! 😭😂😭

invictusdomini

I suspect you meant to say "one and one half" at 2:12

djangogeek

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