4. Consider the system of linear equations below. 1 + 212 - 13 = 2 2x1 + 12 - 13 = 2 4x1 + 212 - 213 = 4 Create the augmented matrix [A b]. Row reduce the augmented matrix to row reduced Ech- elon form so that you can solve Ar = b, where r = I3 [3 marks] 5. Given below is a matrix equation XY = Z, where X is an invertible matrix. Solve the matrix equation to find the matrix Y. Hint: Use Proposition 17.0.1 found in the coursebook. X Z O 1 N H Y -1 3 -2 -2 4 [4 marks]2. (a) Give two distinct 2 x 2 matrices, A and B, whose product is the zero matrix. That is, AB = i} and neither A nor B is the zero matrix. [2 marks] (b) Prove that for any two distinct invertible 2 x 2 matrices, A and B, their product cannot be the zero matrix. [2 marks] {c} Below are three invertible matrices P, Q and R. 3 [l 2 1 a 3 P=[1 2] Q=l1 5] R=[1 1] i. Show that {PQRF = RTQTPT. [2 marks] ii. What restriction should be placed on the value of o? [1 marks] 3. Given below are two matrices, M1 and M2. 2 2 4 16 1 1 2 S M1=21315 M2=Ul 1 1 3 k 5 h. [1 k+2 k+h21 (a) Clearlyr show all row operation steps that mold reduce M1 to M2. [3 marks] (h) Give the values of k and I: that would give the system: i. a unique solution [1 marks] ii. innitelyr many solutions [1 marks] iii. no solution [1 marks]