Let V be a k dimensional subspace (0 k n 1) of R and let F 1 x 1 V and F x V for vectors x 1 , in R Prove that either F 1 F 2 or F 1 F 2 Thus two parallel flats either coincide or are disjoint

Question: Let V be a k-dimensional subspace (0 k n 1) of R and let F 1 = x 1 + V and

Let V be a k-dimensional subspace (0 ≤ k ≤ n – 1) of R" and let F₁= x₁+ V and F = x + V for vectors x₁, in R". Prove that either F₁= F₂or F₁∩F₂= ∅. Thus two parallel flats either coincide or are disjoint.

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