Derive the expression for following questions. Do not write the answers directly.

(a) Let A Rnn, x Rn. Compute (xT Ax)x.

(b) Let x Rn. Prove that ||x||₂ ||x||₁ n||x||₂. (Hint: The Cauchy-Schwarz inequality may come in handy.)

(c)Write down a simple expression for g(x) = sup_{||z||1(a even smaller 1)1} x^Tz. Hint: first prove an upper bound on g(x), then propose a choice of z that achieves the bound.