# 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?

Tags :