For the second-order tensor Cij = uivj: (a) Calculate the principal invariants IC, IIC, and IIIC . Reduce your answer to its simplest form, but leave it in index notation. State the reasons for simplification. (b) If u = ( 1 2 3) and v = (5 10 4) write out the matrix form for Cij. (c) Use the numbers of (b) to validate the answer of (a).