Please show detailed work and explanation! Many thanks!! 1. Show that the functi

Question

Please show detailed work and explanation! Many thanks!!                

                    1. Show that the function A -> ll A ll defined by Lipschitz dependence of the solutions on the initial conditions (if you need this theorem I will gladly                    give it to you) is a norm in the space Mn of n x n matrices with real entries. ( I can give you the definition of norm if you need it)                

                    2. Show that the norm ll * ll defined by Lipschitz dependence of the solutions on the initial conditions (if you need this theorem I will gladly give it to                    you) satisfies ll AB ll <= ll A ll * ll B ll for every A,B in Mn

Explanation / Answer

Please provide the theorems too.

Thanks

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