a) Below is provided part of a matrix representation of an operator, O, using outer product notation. Identify the additional missing outer product terms required to ensure that this operator is a valid quantum mechanical operator. Use the standard basis for the vectors 10 >, |1 >, and |2 >. It is suggested to first translate the operator O into a matrix form, and then figuring out what elements you need to add to the matrix to ensure it is a valid QM operator. 0 =10 >21-2i|1 > 1/ Then, using the completed O matrix, determine which of the following vectors is an eigenvector of 0: [i,1,1], [3,1,4], [i,0,1]. b) The grade distribution for a class could be described using the following wavefunction: Y>= 1/A>+3B>+1C>+0.2/D> where the kets |A >, |B >,|C >, and |D > are orthonormal eigenfunctions of the grading operator G with corresponding eigenvalues G |A >=4/A >, G [B >= 3B >, G IC >= 2/C>, and G D >= 1 D >. Calculate the expected grade of the class, , described by the state |F > by rounding the numerical value you calculate to the nearest integer and converting to the corresponding grade