Hi everybody

I am stuck on this question and hope to get some ideas from u guys

(a) If T: R^m --> R^n is a linear transformation, show that there is a number M such that |T(h)|=< M|h| for h in R^m

(b) Prove that T is continuous

Here is my attempt:

T: R^m --> R^n is a linear transformation if:

T(x+y) = T(x)+T(y) for all x, y in R^m

T(kx) = kT(x) for k is real number

What do I have to do now? and how do you start part b?

Thanks for any suggestions