Orthogonal Basis for Subspace: Find Solution

[hpayandah]

Hi Everyone,
I want to ask if I did this problem correctly.

Homework Statement

Find a orthogonal basis for subspace {[x y z]^T|2x-y+z=0}

Homework Equations

X₁= [3 2 -4]^T, X₂=[4 3 -5]^T

The Attempt at a Solution

Gram-Schmidt:
F1=X1= [3 2 -4]
F2= X2- ((X2.F1)/||F1||²)F1= [4 3 -5]^T + (26/29)[3 2 -4]^T


Thanks in advance.

 

[micromass]

Hi hpayandah!

I don't quite get how you obtained the 26 in the end. Could you explain? (Maybe I just miscalculated it).

 

[hpayandah]

Hi, Thanks for replying, it's the result of:

(X₂ . F₁) / (||F₁||²)

Attached is my work.

 

[micromass]

Yes, that is correct. You wrote X₂ wrong in the OP

 

[hpayandah]

Yes, that is correct. You wrote X₂ wrong in the OP

Appreciated.