Numerical Mathematics Problems

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le ) 2. Consider R² with the norm ||lp, as in Example 1, Section 3. Let T be a matrix operator (a b TE с mapping (R?, I'llp) into (R2, Il·lp). (a) Compute ||T || when b = c and p = 2. (b) Compute ||T || in general. 3. Let M, denote the space of real n x n matrices. For A = (aij) e M, define η(A) = ΣΙail. (a) Show here that || Ax|li s n(A) ||*||1, where x e R" and R" have the norm || xl|1 = {1=1 \xil. (b) Let A, B e Mn. Show that n(AB) s n(A)n(B). (c) Let || A|| be given by Definition 5.8.1 where X = Y = RM with the norm ||*||1. Compare n(A) and || A||. When are they equal?
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