CBSE Guess > Papers > Important Questions > Class XII > 2007 > Maths > Matrices Determinants By Mr. V. Nagarajan Matrices Determinants
O. 1. O. 2. O. 3. Solve the following system of equations by Cramer’s rule: O. 4. O. 5. O. 6. O. 7. Without expanding the determinant show that a+b+c is a factor of the determinant O. 8. Solve the following system of equations by Cramer’s rule: O. 9. O. 10. Without expanding the determinant, prove that O. 11. O. 12. Find a 2x2 matrix, B such that O. 13. Construct a 2x2 matrix a = [aij], whose elements are given by O. 14. Using determinants, find the area of the triangle whose vertices are (-2,4), (2,-6) and (5,4 ). Are the given points collinear? O. 15. Define a symmetric matrix. Prove that O. 16. Using determinants, find the area of the triangle with vertices (-3, 5) (3,-6) & (7,2). O. 17. Express the matrix O. 18. Compute the adjoint of the matrix Q. 19. For matrix O. 20. O. 21. Construct a 2 X 3 matrix whose elements in the ith row and jth column are given by O. 22. Without expanding the determinant, prove that O. 24. Without expanding the determinant, prove that O. 25. Find a matrix X such that 2A+ B+ X = 0, where O. 26. Q. 28. O. 30. From the following equation, find the values of x and y: O. 31. Using properties of determinants, O. 32. Using properties of determinants show that i. ii. O. 33. Find X such that O. 34. Solve by crammer’s rule: 5x-7y+z = 11, 6x-8y-z = 15, 3x+2y –6z =7. O. 35. Show that O. 36. Using properties of determinants show that: O. 37. O. 38. Using cramer’s rule solve the following system of equations: 3x - 2y = 5, x - 3y + 3 = 0. O. 39. Using properties of determinants show that: O. 40. Solve the following system of equations by matrix method:
O. 41. O. 42. O. 43. O. 44. O. 45.F ind O. 46. O. 47. Using properties of determinants, prove that O. 48. Using matrix method solve the following system of linear equations: x + y - z = 1, 3x + y -2z = 3, x - y - z = -1 [CBSE 2004] O. 49. O. 50. Using properties of dets/. prove that O. 51. O. 52. Using properties of determinants, solve for x: O. 53. Using matrix method solve the following system of linear equations: x + y - z = 1, x - y – z = -1, 3x + y-2z = 3. [CBSE 05] O. 54. O. 55. Using matrix method solve the following system of linear equations: x+2y+z = 7, x+3z = 11, 2x - 3y = 1. [CBSE 05] O. 56. Find the value of x, O. 57. Express the matrix O. 58. Using properties of determinants, prove the following: O. 59. Using matrices, solve the following system of equations
O. 60. O. 61. If a, b and c are in A.P. show the following: O. 62. Using matrices, solve the following system of equations
O. 63. O. 64. Using properties of determinats, prove the following: O. 65. Using matrices, solve the following system of equations.
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