Class 12 Maths – RD Sharma Chapter 5 : Algebra of Matrices Very Short Question Answer Solutions (Step-by-Step Guide)

RD Sharma Chapter 5 : Algebra of Matrices Very Short Question Answer Solutions

1. If A = [[2, 1, 4], [4, 1, 5]] and B = [[3, -1], [2, 2], [1, 3]]. Write the orders of AB and BA. Watch Solution
2. If A is an m×n matrix and B is n×p matrix does AB exist ? If yes, write its order. Watch Solution
3. If A = [[4, 3], [1, 2]] and B = [[-4], [3]], write AB. Watch Solution
4. If A = [[1], [2], [3]], write AA^T Watch Solution
5. Give an example of two non-zero 2×2 matrices A and B such that AB = O. Watch Solution
6. If A = [[2, 3], [5, 7]], find A,+,A^T Watch Solution
7. If A = [[i, 0], [0, i]], write A^2 Watch Solution
8. If A = [[cos x, sin x],[-sin x, cos x]], find x satisfying 0 < x < π/2 when A+A^T = I Watch Solution
9. If A = [[cos x, -sin x], [sin x, cos x]], find AA^T Watch Solution
10. If [[1, 0], [y, 5]] + 2[[x, 0], [1, -2]] = I, where I is 2×2 unit matrix. Find x and y. Watch Solution
11. If A = [[1, -1], [-1, 1]], satisfies the matrix equation A^2 = kA, write the value of k. Watch Solution
12. If A = [[1, 1], [1, 1]] satisfies A^4 = λA, then write the value of λ. Watch Solution
13. If A = [[-1, 0, 0], [0, -1, 0], [0, 0, -1]], find A^2 Watch Solution
14. If A = [[-1, 0, 0], [0, -1, 0], [0, 0, -1]], find A^3 Watch Solution
15. If A = [[-3, 0], [0, -3]], find A^4 Watch Solution
16. If [x, 2] [[3], [4]] = 2, find x Watch Solution
17. If A = [aij] is a 2×2 matrix such that aij = i + 2j, write A. Watch Solution
18. Write matrix A satisfying A + [[2, 3], [-1, 4]] = [[3, -6], [-3, 8]]. Watch Solution
19. If A = [aij] is a square matrix such that aij = i^2 – j^2, then write whether A is symmetric or skew-symmetric. Watch Solution
20. For any square matrix write whether AA^T is symmetric or skew-symmetric. Watch Solution
21. If [x, 2] [[3], [4]] = 2 find x Watch Solution
22. If A = [aij] is a 2×2 matrix such that aij = i + 2j, write A. Watch Solution
23. Write matrix A satisfying A + [[2, 3], [-1, 4]] = [[3, -6], [-3, 8]] Watch Solution
24. If A = [aij] is a square matrix such that aij = i^2 – j^2, then write whether A is symmetric or skew-symmetric. Watch Solution
25. For any square matrix write whether AA^T is symmetric or skew-symmetric. Watch Solution
26. If A = [aij] is a skew-symmetric matrix, then write the value of Σi aii. Watch Solution
27. If A = [aij] is a skew-symmetric matrix, then write the value of Σi Σj aij. Watch Solution
28. If A and B are symmetric matrices, then write the condition for which AB is also symmetric. Watch Solution
29. If B is a skew-symmetric matrix, write whether the matrix ABA^T is symmetric or skew-symmetric. Watch Solution
30. If B is a symmetric matrix, write whether the matrix AB A^T is symmetric or skew-symmetric. Watch Solution
31. If A is a skew-symmetric and n∈N such that (A^n)^T = λA^n, write the value of λ Watch Solution
32. If A is a symmetric matrix and n∈N, write whether A^n is symmetric or skew-symmetric or neither or these two. Watch Solution
33. If A is a skew-symmetric matrix and n is an even natural number, write whether A^n is symmetric or skew-symmetric or neither of these two. Watch Solution
34. If A is a skew-symmetric matrix and n is an odd natural number, write whether A^n is symmetric or skew-symmetric or neither of these two. Watch Solution
35. If A and B are symmetric matrices of the same order, wrote whether AB – BA is symmetric or skew-symmetric or neither of the two. Watch Solution
36. Write a square matrix which is both symmetric as well as skew-symmetric. Watch Solution
37. Find the values of x and y, if 2[[1, 3], [0, x]] + [[y, 0], [1, 2]] = [[5, 6], [1, 8]]. Watch Solution
38. If [[x+3, 4], [y-4, x+y]] =[[5, 4], [3, 9]], find x and y. Watch Solution
39. Find the value of x from the following : [[2x – y, 5], [3, y]] = [[6, 5], [3, -2]] Watch Solution
40. Find the value of y, if [[x – y, 2], [x, 5]] = [[2, 2], [3, 5]] Watch Solution
41. Find the value of x, if [[3x + y, -y], [2y – x, 3]] = [[1, 2], [-5, 3]] Watch Solution
42. If matrix A = [ 1, 2, 3], write AA^T Watch Solution
43. If [[2x + y, 3y], [0, 4]] = [[6, 0], [6, 4]], then find x. Watch Solution
44. If A = [[1, 2], [3, 4]], find A + A^T. Watch Solution
45. If [[a + b, 2], [5, b]] = [[6, 5], [2, 2]], then find a. Watch Solution
46. If A is a matrix of order 3×4 and B is a matrix of order 4×3, find the order of the matrix of AB. Watch Solution
47. If A = [[cos α, -sin α], [sin α, cos α]] is identity matrix, then write the value of α. Watch Solution
48. If [[1, 2], [3, 4]] [[3, 1], [2, 5]] = [[7, 11], [k, 23]], then write the value of k. Watch Solution
49. If I is the identity matrix and A is a square matrix such that A^2 = A, then what is the value of (I + A)^2 – 3A ? Watch Solution
50. If A = [[1, 2], [0, 3]] is written as B + C, where B is a symmetric matrix and C is a skew-symmetric matrix, then find B. Watch Solution
51. If A is 2×3 matrix and B is a matrix such that A^T B and BA^T both are defined, then what is the order of B? Watch Solution
52. What is the total number of 2×2 matrices with each entry 0 and 1 ? Watch Solution
53. If [[x, x – y], [2x + y, 7]] = [[3, 1], [8, 7]], then find the value of y. Watch Solution
54. If a matrix has 5 elements, write all possible orders it can have. Watch Solution
55. For a 2×2 matrix A = [aij] whose elements are given by aij = i/j, write the value of a12. Watch Solution
56. If x[[2], [3]] + y[[-1], [1]] = [[10], [5]], find the value of x. Watch Solution
57. If [[9, -1, 4], [-2, 1, 3]] = A + [[1, 2, -1], [0, 4, 9]], hen find matrix A. Watch Solution
58. If [[a – b, 2a + c], [2a – b, 3c + d]] = [[-1, 5], [0, 13]], find the value of b. Watch Solution
59. For what value of x, is the matrix A = [[0, 1, -2], [-1, 0, 3], [x, -3, 0]] a skew-symmetric matrix? Watch Solution
60. If matrix A = [[2, -2], [-2, 2]] and A^2 = pA, then write the value of p. Watch Solution
61. If A is a square matrix such that A^2 = A, then write the value of 7A – (I + A)^3, where I is the identity matrix. Watch Solution
62. If 2[[3, 4], [5, x]] + [[1, y], [0, 1]] = [[7, 0], [10, 5]], find x – y. Watch Solution
63. If [x, 1] [[1, 0], [-2, 0]] = O, find x. Watch Solution
64. If [[a + 4, 3b], [8, -6]] = [[2a + 2, b + 2], [8, a – 8b]], write the value of a – 2b. Watch Solution
65. Write a 2×2 matrix which is both symmetric and skew-symmetric. Watch Solution
66. If [[xy, 4], [z + 6, x + y]] = [[8, w], [0, 6]], write the value of (x + y + z). Watch Solution
67. Construct a 2×2 matrix A=[aij] whose elements aij are given by aij = {|-3i + j|/2, if i≠j (I+j)^2, if i=j Watch Solution
68. [[x + y], [x – y]] = [[2, 1], [4, 3]] [[1], [-2]], then write the value of (x, y). Watch Solution
69. Matrix A = [[0, 2b, -2],[3, 1, 3],[3a, 3, -1]] is given to be symmetric, find the values of a and b. Watch Solution
70. Write the number of all possible matrices of order 2×2 with each entry 1, 2 or 3 Watch Solution
71. If [2, 1, 3] [[-1, 0, -1], [-1, 1, 0], [0, 1, 1]] [[1], [0]. [-1]] = A then write the order of the matrix A. Watch Solution
72. If A = [[3, 5], [7, 9]] is written as A = P + Q, where as A = P + Q, where P is symmetric and Q is skew-symmetric matrix, then write the matrix P. Watch Solution
73. Let A and B be matrices of orders 3 × 2 and 2 × 4 respectively. Write the order of matrix AB. Watch Solution

 

ALGEBRA OF MATRICES – R.D. Sharma Class 12th Math

1. Algebra of Matrices Exercise 5.1 Video Solution
2. Algebra of Matrices Exercise 5.2 Video Solution
3. Algebra of Matrices Exercise 5.3 Video Solution
4. Algebra of Matrices Exercise 5.4 Video Solution
5. Algebra of Matrices Exercise 5.5 Video Solution
6. Algebra of Matrices Very Short Answer Questions (VSAQs) Video Solution
7. Algebra of Matrices Multiple Choice Questions (MCQs) Video Solution