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2 cards from this section. Quick, good the night before a test.
What is the definition of the orthogonal complement?
Think about the vectors that satisfy the zero inner product condition.
If W is a subspace of a vector space V, what does W⊥ represent?
Consider what 'orthogonal' means in terms of the inner product.
What does the orthogonal complement W⊥ consist of?
Consider how orthogonality relates to inner products.
True or False: The orthogonal complement of a subspace W can never include the zero vector.
Think about the property of the zero vector with respect to inner products.
Consider a vector space V = R² and a subspace W = span{(1, 1)}. Find the orthogonal complement W⊥ and describe its geometric representation.
Use the definition of orthogonality and visualize it graphically.
Let W be the set of vectors {(1, 2, 0), (1, 0, 1)} in R³. Determine W⊥ and provide a justification for your findings.
You may want to set up a system of linear equations based on the orthogonality conditions.
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