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

Let [tex]{\bf u}(x) = \begin{bmatrix} u_1(x) \\ u_2(x) \end{bmatrix}[/tex] for [itex]x\in [1,2] [/itex].

I'm asked to find:

[itex]\displaystyle \sup_{\substack{x\in [1,2] }} \| {\bf u} \|[/itex] where [itex]\| {\bf u} \| = \text{max}_j |u_j|[/itex] and am given that [itex]|u_1(x)| \leqslant 5[/itex] and [itex]|u_2(x)| \leqslant 10[/itex].

3. The attempt at a solution

If I was given that [itex]|u_1(x)| = 5[/itex] and [itex]|u_2(x)| = 10[/itex] I'd know how to do it:

[itex]\| {\bf u} \| = \text{max}(|u_1(x)| , |u_2(x)|) = \text{max}(5,10) = 10[/itex]

but how do I use the bounds? Do I say:

[itex]\| {\bf u} \| = \text{max}(|u_1(x)| , |u_2(x)|) \leqslant \text{max}(5,10) = 10[/itex]

and therefore [itex]\displaystyle \sup_{\substack{x\in [1,2] }} \| {\bf u} \| = 10[/itex] ?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Maximums and Supremums - vectors

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**