(1) Determine the sign associated with each of the following permutations of the column indices in the expansion of a 6 x 6 matrix. (a) 652341, (b) 341256, (c) 146523 (2) Using the elementary row or column operations evaluate 4 0 |2 0 3 2 -4 |B = 1 4 |-1 2 |A| = 1 2 0 0 -3 0 3 5 -2 3 -1 6. 1 11 8. -4 az a2 a3 (3) If b by b = 3. find C2 a1 +2b1 3ei az+ 2b2 3c2 az+2b3 3cs b b2 by C2 C3 (4) Determine which of the following matrices are nonsingular. 1 2 0 5 3 4 1 [1 3 2 1 4 -2 5 2 1 -7 2 0 1 2