1. The problem statement, all variables and given/known data From Calculus on Manifolds by Spivak: 1-10 If T:Rm -> Rn is a Linear Transformation show that there is a number M such that |T(h)| [tex]\leq[/tex] M|h| for h[tex]\in[/tex]Rm 2. Relevant equations T is a Linear Transformation => For All x,y [tex]\in[/tex] Rn and scalar c 1. T(x+y)=T(x)+T(y) 2. T(cx)=cT(x) 3. The attempt at a solution Well I didn't get very far but I do know this. The matrix of T with respect to the standard basis is A. Ah=T(h) So we can write what |T(h)| and |h| look like. |T(h)|=sqrt((a11h1+...+a1nhn)2+...+(am1h1+...+amnhn)2) where aij's are the elements in the matrix representation of T, A. |h|=sqrt((h1)2+...+(hn)2) Suggestions, hints and clues are all appreciated!