No written by hand solution and no image Suppose that || · || and ⟨⟨·⟩⟩ are two norms on Rn. We say that the norms || · || and ⟨⟨·⟩⟩ are “comparable norms” if we can find constants c1 and c2 such that for all x ∈ Rn we have the inequalities: ||x|| ≤ c1 ⟨⟨x⟩⟩ and that ⟨⟨x⟩⟩ ≤ c2||x|| Prove that the following norms are comparable: (i) ||·||1 and ||·||2 (ii) ||·||1 and ||·||∞ (iii)||·||2 and||·||∞ Note, it turns out that all norms on Rn are comparable. However, this takes more effort to show as we do not have an explicit formula for a norm in general.

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