4. Problem 4 (a) (1 point) What is the largest possible number of pivots a 4 x 6 matrix can have? Why? (b) (1 point) What is the largest possible number of pivots a 6 x 4 matrix can have? Why? (c) (1 point) Suppose the matrix of coefficients corresponding to a linear system is 4 x 6 and has three pivot columns. How many pivot columns does the augmented matrix have if the linear system is inconsistent? 5. Problem 5 Which of the following matrices are in rref? If a matrix is not in this form, explain which part of the definition is violated. (a) (1 point) 0 3 -2 1 5 60 0 0 (b) (1 point) 0001 010 0 O 010 6. Problem 6 Transform each of the following matrices to rref: 1 3 7 (a) (1 point) 0 1 6 2 0 1 5 (b) (1 point) ONE7. Problem 7 Solve each of the following systems (if possible) by using Gauss Jordan elimina tion: (a) (1 point) 2x +y - 32 = 1 5x + 2y - 62 = 5 3.x - y - 4z = 7 (b) (1 point) x + 2y + 3z + 4w = 5 x + 3y + 52 + 7w =11 x - 2- 2w =-6