Murphy Vaughan
01/13/2024 · Elementary School
Question 2 Let \( V=R^{2} \), and let \( \|(a, b)\|=\max \{|a|,|b|\} \), for \( (a, b) \in V \). Prove that \( \|\cdot\| \) as defined here is a norm on \( V \).
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To prove \( \|\cdot\| \) is a norm on \( V \), we verify non-negativity, definiteness, homogeneity, and triangle inequality. All properties are satisfied, hence \( \|\cdot\| \) is a norm on \( V \).
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