Problem 3. (20%) Consider the n by n matrix 2 1 2-(n-2) 2 2-(n-3) 2-in-2) 2-1 2-2 2-3 2-4 1 2-1 2-2 2-3 2 2-1 2-2 2-(n-2) 2-(n-3) 2-in-4) 1 2-1 2-2 2-3 2-4 2-5 2-(n-2) 2 Write down this matrix for the case n=5. Use the Banach Lemma (with the matrix infinity-norm) to show that A, is invertible for any positive integer n. Also use the Banach Lemma to derive a suitable upper bound on the infinity-norm of A