Question: Let A be an n x n matrix and x Rn. Prove (a) ||Ax||2 n1/2 ||A||||x||2 (b) n-l/2||A||2 ||A|| n1/2||A||2

Let A be an n x n matrix and x ∈ Rn. Prove
(a) ||Ax||2 ≤ n1/2 ||A||∞||x||2
(b) n-l/2||A||2 ≤ ||A||∞ ≤ n1/2||A||2

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