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Matrix Problem Solving · CSEC Mathematics

32 past-paper questions on Matrix Problem Solving, part of VECTORS AND MATRICES, from every CSEC Mathematics paper on Quelpr.

Practise Matrix Problem Solving
  1. 14(a)5 marks· CSEC Mathematics · 2003 (Specimen) · Paper 2Use a matrix method to solve the equations: 3x - y = 5 and 2x + 5y = 9.
  2. 10(a)(i)b)2 marks· Mathematics Q10 10(a)(i)b)Hence, find the values of h and k that satisfy the matrix equation [-1 3; 4 h] [k; 5] = [0; 0].
  3. 10(a)(ii)3 marks· Mathematics Q10 10(a)(ii)Using a matrix method, solve the simultaneous equations 2x + 3y = 5 and -5x + y = 13.
  4. 11(a)(i)2 marks· Mathematics Q11 11(a)(i)Write the following simultaneous equations 3x + 2y = -1 and 5x + 4y = 6 in the form AX = B, where A, X and B are matrices.
  5. 11(a)(i)3 marks· Mathematics Q11 11(a)(i)Determine the values of a, b, c and d.
  6. 11(a)(ii)2 marks· Mathematics Q11 11(a)(ii)State the coordinates of Z such that Z(x,y) → Z'(5,1) under the transformation, M.
  7. 11(a)(ii)4 marks· Mathematics Q11 11(a)(ii)The matrix T maps the point (a, b) onto the point (4, 9). Determine the values of a and b.
  8. 11(a)(ii)4 marks· Mathematics Q11 11(a)(ii)Use a matrix method to solve for x and y.
  9. 11(a)(iii)2 marks· Mathematics Q11 11(a)(iii)Write ((x), (y)) as the product of TWO matrices.
  10. 11(a)(iv)2 marks· Mathematics Q11 11(a)(iv)Hence, calculate the values of x and y.
  11. 11(b)2 marks· Mathematics Q11 11(b)Express the equations 4x - 2y = 0 and 2x + 3y = 4 in the form AX = B, where A, X and B are matrices.
  12. 11(b)(i)1 mark· Mathematics Q11 11(b)(i)Write the following pair of simultaneous equations as a matrix equation.
  13. 11(b)(ii)2 marks· Mathematics Q11 11(b)(ii)Write the solution of your matrix equation in (b)(i) as a product of two matrices.
  14. 11(b)(iii)5 marks· Mathematics Q11 11(b)(iii)Use a matrix method to solve for r, s, t and u in the equation [[2, 1], [4, 3]] * [[r, s], [t, u]] = [[2, 1], [4, -1]].
  15. 11(b)(iii)3 marks· Mathematics Q11 11(b)(iii)Use the inverse of (2, -4; 1, -3) to solve for x and y in the matrix equation (2, -4; 1, -3) * (x, y) = (12, 7).
  16. 11(c)(ii)3 marks· Mathematics Q11 11(c)(ii)Using a matrix method, find the values of x and y in the equation (4 2; 1 1) (x; y) = (8; 3).
  17. 11(c)(iii)2 marks· Mathematics Q11 11(c)(iii)Given that (5 -1; 0 3)(x y) = (6 9), calculate the values of x and y.
  18. 11(c)(iv)3 marks· Mathematics Q11 11(c)(iv)Hence, calculate the values of x and y for which (4, 1; 3, 2) * (x, y) = (1, 2).
  19. 14(a)(ii)4 marks· Mathematics Q14 14(a)(ii)Calculate the values of x and y for which M * [[x], [y]] = [[12], [1]].
  20. 14(a)(iv)1 mark· Mathematics Q14 14(a)(iv)Pre-multiply both sides of the following matrix equation by M⁻¹: [[2, 5], [7, 15]] * [[x], [y]] = [[-3], [17]]. Hence solve for x and y.
  21. 14(a)(iv)1 mark· Mathematics Q14 14(a)(iv)Find the value of a, b, c and d given that 3A + B⁻¹ = C.
  22. 14(a)(iv)a)2 marks· Mathematics Q14 14(a)(iv)a)Write the total profit made as a product of two matrices.
  23. 14(a)(iv)b)2 marks· Mathematics Q14 14(a)(iv)b)Calculate the total profit made on the transaction.
  24. 14(b)(i)5 marks· Mathematics Q14 14(b)(i)Express the pair of equations in the form AX = B, where A, X and B are matrices.
  25. 14(b)(i)2 marks· Mathematics Q14 14(b)(i)Write the equations in the form AX = B where A, X and B are matrices.
  26. 14(b)(ii)6 marks· Mathematics Q14 14(b)(ii)Hence, calculate the value of x and of y for which M(x; y) = (12; -8).
  27. 14(b)(ii)c)5 marks· Mathematics Q14 14(b)(ii)c)Use the matrix A⁻¹ to solve for x and y.
  28. 14(b)(iii)5 marks· Mathematics Q14 14(b)(iii)Evaluate: A⁻¹B.
  29. 14(b)(iv)4 marks· Mathematics Q14 14(b)(iv)Using a matrix method, solve the pair of simultaneous equations: 2x - y = 0 and x + 3y = 7.
  30. 14(c)(i)2 marks· Mathematics Q14 14(c)(i)Write the following simultaneous equations in the form AX = B where A, X and B are matrices: 11x + 6y = 6 and 9x + 5y = 7.
  31. 14(c)(ii)4 marks· Mathematics Q14 14(c)(ii)Hence, calculate the value of x and the value of y for which 3x - y = 5 and 2x + 5y = 9.
  32. 14(c)(ii)2 marks· Mathematics Q14 14(c)(ii)Hence, write the solution for x and y as a product of two matrices.

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