Use the Gram-Schmidt process to find an orthonormal basis

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Q. Let S={u_1,u_2,u_3 } with the vectors defined below. S is a basis for R3. Use the Gram-Schmidt process to get an orthonormal basis.

u_1=(1,1,1) u_2=(0,1,1) u_3=(0,0,1)

Every nonzero finite-dimensional inner product space has an orthogonal basis.

#Orthonormal #LinearAlgebra #Projection
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At 2:44, 1-(2/3) is 1/3. So v3 will be (0, -1/root 2, -1/root 2)

bharathchandrapanasa
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Finally somebody that actually explains how to do it in a simple way! Thank you!

aleksandrailieva
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Sir, you just saved my quizzes score, thank you for this simple and easy to understand guide

goldenrkivee
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OMG
your sum came to my exam same values

aravindthulasi
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This video helps me a lot...Thank You sir

mahigour
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Very useful video, but I just wanted to ask why at 1:22 did you mention the ^2 on the denominator if you were going to take norm and square root it anyway? Isn't is pointless to denote ||v||^2 if the square and square root cancel out? I'm definitely missing something here.

VodkaTheAntiAlcoholic
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at 2:43, how is 1-2/3 = -1/3? isn't the same as 3/3-2/3=1/3?
Am I missing something?

itzel_ixchel
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thanks sir for the help. but I don't understand why you ignored the negative sign.

newtonngigi
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I have seen where you ignore minus sign!!why that ?or is a mistake 🤷‍♀️

tuyizereangelique
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Condom ad was coming during my study time🙂🙂🙂🙂

baka
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If you make every number a one or a zero, how is anyone supposed to keep track of which numbers go together? Key steps are being glossed over because 1x1 is obviously 1. Why is every video on this subject as well as my professors so lazy?

Jostan
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There was a mistake when subtracting the numbers.1-2/3 must be equal to 1/3 and not -1/3

KingsPhiri-oh
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sir or anyone please can you explian abuout the last one at sub3 why the result is (0, -1/2, 1/2)??

yonafat_