Respuesta :
(0, 0, 1) is not in the orthogonal complement of X. Then the given statement is false.
What is an orthogonal complement?
Orthogonal complements comprise topological spaces that are perpendicular to each other. The orthogonal counterpart of a subset, regardless of how that is selected, is a domain, that is, a set bounded in terms of taking different combinations. Proposition Assume that is a vector space.
Consider {(0, 0, 1), (0, 1, 1), (1, 1, 1)}
Clearly {u, v, w} is linearly independent .
Let X = span {v, w}
Clearly, a vector v is an orthogonal complement of X. If
<v, x> = 0 ∀ x ∈ X
Here, in R³ we can take the dot product as the inner product.
Consider (0, 1, 1), clearly (0, 1, 1) ∈ X take u·v that is (0, 0, 1)·(0, 1, 1) will be
→ 1 ≠ 0
Therefore, (0, 0, 1) is not in the orthogonal complement of X. Hence, the given statement is false.
More about the orthogonal complement link is given below.
https://brainly.com/question/23555459
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