QUESTION 1 (4 marks) a) If A = (-²-3) 7-8/ Determine AxB. and B = ( _ _ $) -3-4 b) Use MATLAB to verify your answer. QUESTION 2 (6 marks) a) Use matrices to solve the simultaneous equations: (4x - 3y = 17 x+y=-1 b) Use MATLAB to verify your answers. QUESTION 3 (4 marks) a) Calculate the determinant of the following 3x3 matrix. 254 -5 b) Use MATLAB to verify your answer. 1 D. 31 0 NO 2 (2 marks) (2 marks) (4 marks) (2 marks) (3 marks) (1 mark)
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Step 1: To determine AxB, we need to multiply each element of matrix A by the corresponding element in matrix B and then sum the products. Show more…
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Question 3 (a) Given the matrices, P = [3 -2; 7 -4], Q = [-4 2; -7 3], find (i) PQ (ii) QP (iii) Write a possible relationship between P and Q. (b) (i) Find a and b if 4[a 2; -1 3a] + [b -2; 5 -b] = [7 6; 1 1] (ii) If A = [3 2; -1 1] and B = [0 -4; -2 8], find matrices X such that 2A + X = B (c) Given A = [0 1; 2 3]. (i) Show that A is non-singular. (ii) Find B such that BA^2 = A (d) The matrix A = [3 -5; -1 2] is the inverse of B = [2 5; 1 3]. Verify this statement. [Hint: You need to show that AB = BA = I]
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Question B2 Consider the system of equations, x + 2y - z = 7 -3y + 2x - 4z = -3 x + y + z = 0 i. Put the equations in matrix form, that is find matrix A and vector B Ax = B (4 marks) ii. Compute the transpose AT and 2A + A (7 marks) iii. Compute A2 A3 (8 marks) iv. Compute det (A) (7 marks) v. Solve for the unknowns x, y and z (8 marks)
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