(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that the Euclidean and supremum norms are equivalent norms on R^{2}

3. The attempt at a solution

The Euclidean Norm is

[tex]\left|\left|[/tex]X[tex]\left|\left|[/tex]_{1}= [tex]\sqrt{x1^2 + x2^2}[/tex]

The Supremum norm is

[tex]\left|\left|[/tex]X[tex]\left|\left|[/tex]_{[tex]\infty[/tex]}= max ([tex]\left|[/tex]x1[tex]\left|[/tex],[tex]\left|[/tex]x2[tex]\left|[/tex])

so for them to be equivalent:

a([tex]\sqrt{x1^2 + x2^2}[/tex])[tex]\leq[/tex] max ([tex]\left|[/tex]x1[tex]\left|[/tex],[tex]\left|[/tex]x2[tex]\left|[/tex]) [tex]\leq[/tex] b([tex]\sqrt{x1^2 + x2^2}[/tex])

I think i'm going right with this?

im not sure how to work with the supremum norm in the middle?

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# Homework Help: Equivalent norms

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