Show that $U := \{ v ∈ \Bbb R^n : ∀ u ∈ U : 〈 v , u 〉 = c \} $ is an affine subspace

by Amerov   Last Updated November 18, 2018 14:20 PM

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?



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