MATH221 December 2007
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Question 06 (a)
Explain why forms a basis for .
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To see why forms a basis for , we recall two facts:
- Orthogonal vectors are linearly independent.
- A linearly independent list of length n in a vector space of dimension n is a basis.
Since the two vectors comprising are orthogonal, is a linearly independent list of length 2 in .
Therefore, by the two bulleted points above, is a basis for .
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