Suppose U is a 3 × 3 upper triangular matrix, with entries and L is a 3 × 3 lower triangular matrix with entries aij, bij Then det U = (Enter the value of the determinant in terms of the matrix entries aij, where aij is entered as a_ij) det L = (Enter the value of the determinant in terms of the matrix entries bij, where bij is entered as b_ij) Prove your answer. (This part will be graded after the due date)

1. (a) What (b) What are the seven 2. Consider you have a A matrix as below: 213 A = 1 3 412 12 (b) (40 points) What is the determinant of A matrix, that is to say AA? (a) (30 points) What is the transpose (A') of the matrix?