Show that $U := { v ∈ Bbb R^n : ∀ u ∈ U : 〈 v , u 〉 = c } $ is an affine subspace
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Let $c∈Bbb R$ and $U⊂Bbb R^n$ , $U ne∅$ ( $U$ is a nonempty subset). Further let $〈·,·〉:Bbb R^n×Bbb R^n→Bbb R$ be the standard inner product. Define $$U := { v ∈ Bbb R^n : ∀ u ∈ U : 〈 v , u 〉 = c } .$$ Show that $Uc$ is an affine subspace. I think I should use the Inner standard product. Can someone help me to solve it ? how the begin should be?
linear-algebra affine-geometry
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edited Nov 18 at 14:14
asked Nov 18 at 13:55
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