- #1
Cassi
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Homework Statement
Find an orthonormal basis for the subspace of V4 spanned by the given vectors.
x1 = (1, 1, 0, 1)
x2 = (1, 0, 2, 1)
x3 = (1, 2, -2, 1)
Homework Equations
Gram-Schmidt Process
The Attempt at a Solution
I have used the Gram-Schmidt process but seem to be running into trouble. Here is what I did:
y1 = x1 = (1, 1, 0, 1)
y2 = x - y1 = (1-1, 0-1, 2-0, 1-1) = (0, -1, 2, 0)
y3 = x3 - y1 + y2 = (1-1+0, 2-1-1, -2-0+2, 1-1+0) = (0, 0, 0, 0)
Now I used these and their norms to find the basis {y1, y2}
y1 / lly1ll = 1/sqrt(3) (1, 1, 0, 1)
y2 / lly2ll = 1/sqrt(5) (0, -1, 2, 0)
Therefore, {1/sqrt(3) (1, 1, 0, 1), 1/sqrt(5) (0, -1, 2, 0)} from my work. However, my book says the answer is {(1/3)(1/sqrt(3)(1, 1, 0, 1), 1/sqrt(42) (1, -2, 6, 1)} which is very different than my answer. Where am I going wrong?