Linear Algebra - Gram Schmidt & Normalization - Error in Sol

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SUMMARY

The discussion centers on the Gram-Schmidt process for finding an orthonormal basis for the column space of matrix A. The user initially believes there is an error in the calculation of the norm of vector A_2, specifically questioning the normalization of q_2. The user calculates ||A_2|| as 2, while the answer key suggests it is 3. Upon further review, the user confirms their calculation was correct, and the answer key was indeed incorrect.

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  • Familiarity with vector norms and their calculations
  • Knowledge of linear algebra concepts, specifically column spaces
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YoshiMoshi
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Homework Statement



So I think I found an error in the solution were it attempts to find q_2^

I'm asked find the orthornomal basis for the column space of matrix A.

equation 1.PNG


Homework Equations

The Attempt at a Solution


[/B]
My question is in what it puts for q_2^

equation 2.PNG

A_2 = [4/3 4/3 -2/3]^T
||A_2|| = sqrt((4/3)^2 + (4/3)^2 + (-2/3)^2) = 2

but in the answer key since
q_2 = A_2/||A_2|| it's implying that ||A_2|| = 3 but I calculate 2. Am I doing something wrong?

Thanks for your help.
 
Last edited:
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Oh I see that it's correct my bad
 

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