Let V be a vector space over F field and is nonzero linear functional. So for every and . Show that for every is a hyperplane.

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- Nov 27th 2011, 06:16 AMgotmejerryQuestion about hyperplane
Let V be a vector space over F field and is nonzero linear functional. So for every and . Show that for every is a hyperplane.

Thank you! - Nov 27th 2011, 06:30 AMHallsofIvyRe: Question about hyperplane
It's fairly straight forward isn't it? I would first look at . It's easy to show that is a subspace. Now, given any other Let y be a single vector such that and show that for any x in , x- y is in .