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Let W be the subspace of V4(R) spanned by the following set of vectors...© BrainMass Inc. brainmass.com December 24, 2021, 7:17 pm ad1c9bdddf
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Let W be the subspace of V4(R) spanned by the following set of vectors:
Use the Gram-Schmidt orthogonalisation process to find an orthogonal basis for W. Find also an orthonormal basis for W.
The Gram-Schmidt Theorem:
Given a basis for subspace W of Vn define:
Then is an orthogonal basis of W and has the same span as
We shall use the standard inner product:
In our case:
In the next step we have:
Continued on next page
Thus the orthogonal base is:
The orthonormal basis is defined as the basis vectors divided by their length:
We already know that:
Therefore the orthonormal basis is:
In column form:© BrainMass Inc. brainmass.com December 24, 2021, 7:17 pm ad1c9bdddf>