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Let [math]A=\{A_{i,j}\}_{\substack{1\le i\le n \\ 1\le j \le m}}[/math] be a random matrix such that its entries are \iid sub-Gaussian random variables with variance proxy [math]\sigma^2[/math].

1. Show that the matrix [math]A[/math] is sub-Gaussian. What is its variance proxy?
2. Let [math]\|A\|[/math] denote the operator norm of [math]A[/math] defined by
   [[math]] \max_{x \in \R^m}\frac{|Ax|_2}{|x|_2}\,. [[/math]]
   Show that there exits a constant [math]C \gt 0[/math] such that
   [[math]] \E\|A\|\le C(\sqrt{m}+\sqrt{n})\,. [[/math]]