Given the kets 1), 12), such that (11) = 2, (1/2) = i, (2/2) = 3, show that they are linearly independent. (b) (10 points) Consider the vector space spanned by 1) and 2). Given the operator = |u) (v] where |u) = 1) + i 2) and |v) = 1) - i|2), find the matrix representing the adjoint operator At in the 1), 2) basis. Given the kets 1), 12), such that (11) = 2, (1/2) = i, (2/2) = 3, show that they are linearly independent. (b) (10 points) Consider the vector space spanned by 1) and 2). Given the operator = |u) (v| where |u) = 11) + i 2) and |v) = 1) - i|2), find the matrix representing the adjoint operator At in the 1), [2) basis.