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anonymous
 5 years ago
Let a be a fixed nonzero vector in Rn.
(a) Show that the set of S of all vectors x such that a dot x = 0 is a subspace of Rn.
(b) Show that if k is a nonzero real number, then the set A of all vectors x such that a dot x = k is not a subspace.
Thanks in advance.
anonymous
 5 years ago
Let a be a fixed nonzero vector in Rn. (a) Show that the set of S of all vectors x such that a dot x = 0 is a subspace of Rn. (b) Show that if k is a nonzero real number, then the set A of all vectors x such that a dot x = k is not a subspace. Thanks in advance.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Well (a) is just the nullspace of the vector space characterized by A. (b) is solving a system of equations in which the space characterized is not closed under addition. I think.
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