Question: 3. Consider the function | . pi : R2 -> R defined as follows: for any c = (21, 12) E R2, set lap =(a)

3. Consider the function | . pi : R2 -> R defined as follows: for any c = (21, 12) E R2, set lap =(a) Find a symmetric matrix A c R*2 such that for all a e R-. (b) Show that A above is positive definite (see Definition 2.4 from the lecture notes). (c) Show that | . | pi : R' -> R is a norm. Hints: (b) Use Problem 2(b). (c) Use Lemma 2.3. from the lecture notes

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