Orthogonal Basis for Subspace: Find Solution

  • Thread starter Thread starter hpayandah
  • Start date Start date
  • Tags Tags
    Basis Orthogonal
Click For Summary

Homework Help Overview

The problem involves finding an orthogonal basis for a subspace defined by the equation 2x - y + z = 0. The original poster presents two vectors, X1 and X2, and describes their application of the Gram-Schmidt process to achieve orthogonality.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply the Gram-Schmidt process to the given vectors. One participant questions the calculation of a specific coefficient, while another confirms the correctness of the original poster's approach.

Discussion Status

The discussion is active, with participants engaging in clarifying specific calculations and confirming the accuracy of the presented work. There is no explicit consensus on the correctness of the original poster's vectors, as one participant points out a potential error in the notation.

Contextual Notes

There is a mention of a possible misrepresentation of one of the vectors in the original post, which may affect the overall understanding of the problem.

hpayandah
Messages
18
Reaction score
0
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.
 
Physics news on Phys.org
Hi hpayandah! :smile:

I don't quite get how you obtained the 26 in the end. Could you explain? (Maybe I just miscalculated it).
 
Hi, Thanks for replying, it's the result of:

(X2 . F1) / (||F1||2)

Attached is my work.
 

Attachments

  • 20110709_015.jpg
    20110709_015.jpg
    30.3 KB · Views: 462
Yes, that is correct. You wrote X2 wrong in the OP :smile:
 
micromass said:
Yes, that is correct. You wrote X2 wrong in the OP :smile:
Appreciated.
 

Similar threads

Minimize integral using orthogonal basis
  • · Replies 2 ·
Replies
2
Views
1K
Find the basis of a vector subspace of R^2,2
  • · Replies 9 ·
Replies
9
Views
3K
Determine a basis for kernel/nullspace
  • · Replies 3 ·
Replies
3
Views
2K
I cannot make the Gram-Schmidt procedure work
  • · Replies 16 ·
Replies
16
Views
3K
Linear Transformation (Image, Kernel, Basis, Dimension)
  • · Replies 24 ·
Replies
24
Views
3K
Eigenvectors and orthogonal basis
  • · Replies 2 ·
Replies
2
Views
2K
Is there a better way to find the number of integer solutions
  • · Replies 5 ·
Replies
5
Views
3K
Finding the Orthogonal Complement
  • · Replies 3 ·
Replies
3
Views
2K
Orthogonal projection over an orthogonal subspace
  • · Replies 9 ·
Replies
9
Views
2K
Finding a complementary subspace ##U## | Linear Algebra
  • · Replies 4 ·
Replies
4
Views
2K