Orthogonal Complements | How to Find a Basis for "W Perp" [Passing Linear Algebra] 

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at 6:33 you don't explain how you get to those numbers that follow. You seemed to skip a step.

finally got the concept.. thanks

If You have the vector (a, b, c) then it is orthogonal to all of the vectors on the plane in R^3 defined by ax + by +cz= 0, because (a, b, c) •(x, y, z) = 0. Also if you have the plane in r^3 given by ax +by +cz =0, then the vector (a, b, c) is orthogonal to all the vectors on this plane. Did you show this method to find the orthogonal compliment because it is generalizable to higher dimensions?

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You said that W perp is perpendicular to the original 1/2*x line, but there are infinite lines that are perpendicular. Is W perp the one you chose because it goes through the origin because vector spaces and subspaces must contain the 0 vector?

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At 6:44 shouldn't it be -z since our x component = 3y - z or is it always a + sign

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compliment is different from complement

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wait a minute, at 5:24 you said that dim of w is 2 and dim of w^orth is equal to 1, hence dimw + dimw^orth=3 which is different from dimW=2

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dont you have to normalize in the end?

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This video is very orthogonal. I'll give you that.

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why did you transpose the basis at 8:50 ???

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Video starts at 00:30

And how does y = y and z = z. There is no logical transition. It might seem obvious, but there are skipped steps. Pretend you are creating a video that explains this to a child.

Actually, (W⊥)⊥ ⊇ W, not equal to W, right?