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. then verify that A . A’ = I. O. 6.then find k so that: A^{2} = 8A + kI. 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. show that (AB)’ = B’A’. O. 10. Without expanding the determinant, prove that O. 11.verify that (AB)’ = B’A’. 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 for is a symmetric matrix where A’ is transpose of A. O. 16. Using determinants, find the area of the triangle with vertices (3, 5) (3,6) & (7,2). O. 17. Express the matrix as the sum of the symmetric and skew  symmetric matrix. O. 18. Compute the adjoint of the matrix and verify that A.(adj A)= A I. Q. 19. For matrix where A’ is the transpose of the matrix A. O. 20.find a matrix C such that A + B+C is a zero matrix. 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.show that AB¹ BA. Q. 28. prove that A + AT is a skew symmetric where AT denotes the transpose of A. 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: 5x7y+z = 11, 6x8yz = 15, 3x+2y –6z =7. O. 35. Show that satisfies the equation x^{2} 3x  7 = 0. Thus, find A^{1.} O. 36. Using properties of determinants show that: O. 37. verify A^{2} 4A  I = 0 where hence find A^{1}. 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. If find A^{1}. Using A^{1}, solve the following system of equations: x  2y = 10, 2x + y + 3z = 8, 2y + z = 7. O. 42. If find A^{1}. Using A^{1}, solve the following system of equations: 8x4y+z=5, 10x + 6z =4, 8x + y + 6z = 5/2 O. 43. If find A^{1} and hence prove that: A^{2} 4A –5I = 0. O. 44. Find Also, show that O. 45.F indHence, find the following system of equations: x+2y+5z=10, xy+2 = 0, 2x + 3y  z + 11 =0. 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.prove that A^{2};  4A – 5I = 0. [CBSE 2004] O. 50. Using properties of dets/. prove that O. 51. show that f(A)= 0. [CBSE 05] 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 + y2z = 3. [CBSE 05] O. 54. then prove by principle of Mathematical induction that 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 as the sum o a symmetric and the skew symmetric matrix. [CBSE 2006] O. 58. Using properties of determinants, prove the following: O. 59. Using matrices, solve the following system of equations
O. 60. show that A^{2} – 12A + I = 0. Hence find A1. [CBSE 06] 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. find the values of a and b such that A^{2} + Aa + b = 0. hence find A^{1}. [CBSE 06]. O. 64. Using properties of determinats, prove the following: [CBSE 06] O. 65. Using matrices, solve the following system of equations.

