Problem 2. (6+4 points) (i) Let n > 3. Suppose that A = (aj) is an n x n matrix such that aij =i+j. Calculate det (A). Hint: You may want

to first compute the determinant for smaller size matrices (for n = 3,4) of this kind to guess the answer in general. If you make a correct guess, you may employ an equivalent criterion of invertibility of matrices to establish your hypothesis. (ii) Let u₁ = (2a², a, −1), U₂ = (0, 1, a), us = (a, 0, 1) where a is an unknown constant. Determine the value(s) of a so that span{u₁, U2, U3} = R³.