This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 3 Matrices – Quiz 5 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 3 Matrices Quiz 5 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. *IfA isany square matrix and A' is transpose of its. Then A-A' isalso a matrix of type A) *Skew-symmetric Matrix. B) *Non-diagonal Matrix. C) *Non-Square Matrix. D) *DiagonalMatrix. Show Answer Correct Answer: A) *Skew-symmetric Matrix. 2. Una matriz invertible debe ser cuadrada A) Cierto. B) Falso. C) All the above. D) None of the above. Show Answer Correct Answer: A) Cierto. 3. A is not a symmetric matrix if A' = A. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 4. When is a matrix A said to have a non-zero solution A) If |A|=0. B) If rank of A is 1. C) If |A| not equal to 0. D) If rank of A is 0. Show Answer Correct Answer: A) If |A|=0. 5. If det(A) is zero, then the matrix is ..... A) Non-determinant matrix. B) Singular matrix. C) Null matrix. D) None of the above. Show Answer Correct Answer: B) Singular matrix. 6. Tim will start a lawn mowing service. His expenses will be $ 400 to purchase a lawnmower and $ 1.50 per lawn for gas. His income will be $ 20 per mowed lawn. The profit equation for this scenario before being simplified would be: A) $P=20x-\left(1.50x+400\right)$. B) $P=20x-1.50x+400$. C) $P=1.50x+400$. D) $P=20x$. Show Answer Correct Answer: A) $P=20x-\left(1.50x+400\right)$. 7. Classify the matrix [[0, 0], [0, 0]] by its type. A) Zero matrix. B) Identity matrix. C) Diagonal matrix. D) Symmetric matrix. Show Answer Correct Answer: A) Zero matrix. 8. A matrix of order $3\times3$ A) Zero Matrix. B) Scalar Matrix. C) Square Matrix. D) Diagonal Matrix. Show Answer Correct Answer: C) Square Matrix. 9. What kind of a solution exists for a system of linear equations if n=r, where n is number of unknowns and r is the rank A) Infinitely many solutions. B) Zero solution. C) Unique solution. D) No solution. Show Answer Correct Answer: C) Unique solution. 10. Solve the following system of equations x-y + z = 4, x-2y + 2z = 9 and 2x + y + 3z = 1. A) X =-4, y =-3, z = 2. B) X = 2, y = 4, z = 6. C) X =-1, y =-3, z = 2. D) X = 3, y = 6, z = 9. Show Answer Correct Answer: C) X =-1, y =-3, z = 2. 11. A matrix has rank r if A) I) It has at least one non-zero minor of order r. B) Ii) Every minor of order higher than r vanishes. C) Both (i) and (ii). D) None of these. Show Answer Correct Answer: C) Both (i) and (ii). 12. Non-trivial solution X of the equation AX=$\lambda$X is called A) I) Eigen values. B) Ii) Eigen vectors. C) Both (i) and (ii). D) None of these. Show Answer Correct Answer: B) Ii) Eigen vectors. 13. En una matriz nula todos los elementos son ceros A) Verdadero. B) Falso. C) All the above. D) None of the above. Show Answer Correct Answer: A) Verdadero. 14. Inverse of a square matrix is ..... if it exists A) Different. B) Exists. C) Unique. D) None of the above. Show Answer Correct Answer: C) Unique. 15. Si tengo una matriz A sus elementos se nombran con la letra A) A. B) B. C) B. D) A. Show Answer Correct Answer: A) A. 16. Calculate the product of the matrices [[1, 0], [0, 1]] and [[5, 6], [7, 8]]. A) [[5, 6], [7, 8]]. B) [[5, 7], [6, 8]]. C) [[1, 0], [0, 1]]. D) [[12, 14], [16, 18]]. Show Answer Correct Answer: A) [[5, 6], [7, 8]]. 17. The area of a triangle with vertices (-3, 0), (3, 0) and (0, k) is 9 sq. units. The value of k will be A) -9. B) 9. C) 6. D) 3. Show Answer Correct Answer: D) 3. 18. If A and B are matrices of the same order, then AB$^{T}$-BA$^{T}$ is a: A) Null matrix. B) Symmetric matrix. C) Unit matrix. D) Skew symmetric matrix. Show Answer Correct Answer: D) Skew symmetric matrix. 19. What always comes first in reference to matrix order? A) Column. B) Row. C) Dimension. D) Element. Show Answer Correct Answer: B) Row. 20. According to Cayley-Hamilton Theorem, state which of the following is TRUE. A) Every square matrix does not satisfy its own characteristic equation. B) Every square matrix satisfies its own characteristic equation. C) Every matrix satisfies its own characteristic equation. D) Every skew matrix satisfies its own characteristic equation. Show Answer Correct Answer: B) Every square matrix satisfies its own characteristic equation. 21. Determine the determinant of the matrix K = [[-2, 3, 1], [4, 2, -5], [1, 0, 3]]. A) -65. B) -53. C) 0. D) 11. Show Answer Correct Answer: A) -65. 22. The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are Rs 80, Rs 60 and Rs 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra. A) 20160. B) 20106. C) 20100. D) NONE OF THE ABOVE. Show Answer Correct Answer: A) 20160. 23. Identify the order of the matrix [[1, 2, 3]]. A) 1x3. B) 1x1. C) 3x1. D) 2x2. Show Answer Correct Answer: A) 1x3. 24. The plural of matrix is A) Matrixes. B) Matrices. C) Matrixces. D) Matrixs. Show Answer Correct Answer: B) Matrices. 25. An IDENTITY MATRIX is an example of SCALAR MATRIX . A) TRUE. B) FALSE. C) All the above. D) None of the above. Show Answer Correct Answer: A) TRUE. 26. Derivative of 8$^{x}$ w.r.t. x = A) 1/8. B) 8$^{x}$ log 8. C) 8$^{x}$/log 8. D) 1/x. Show Answer Correct Answer: B) 8$^{x}$ log 8. 27. If A is a singular matrix of order 3 and 2, 3 are two eigenvalues find the 3rd eigenvalue. A) 6. B) 0. C) 2. D) 3. Show Answer Correct Answer: B) 0. 28. If a classroom seating arrangement is obtained by changing the respective rows into columns, then we get ..... of the classroom. A) Negative. B) Inverse. C) Transpose. D) None of these. Show Answer Correct Answer: C) Transpose. 29. How is the order of a matrix identified? A) Row x Column. B) Row only. C) Column x Row. D) Column only. Show Answer Correct Answer: A) Row x Column. 30. Integral of logx = A) X-xlogx. B) Xlogx-x. C) Logx-x. D) 1/x. Show Answer Correct Answer: B) Xlogx-x. 31. Integral of Sin 9x = A) (-Cos 9x)/9. B) 9 Cos 9x. C) -9 Cos 9x. D) (Cos 9x)/9. Show Answer Correct Answer: A) (-Cos 9x)/9. 32. What is a rectangular matrix? A) Number of rows is more than the number of columns. B) Number of rows is 1. C) Number of rows is not equal to the number of columns. D) Number of columns is 1. Show Answer Correct Answer: C) Number of rows is not equal to the number of columns. 33. En una matriz $a_{ij}$ A) $i$ $j$. B) $i$ $j$. C) $i$ $j$. D) $i$ $j$. Show Answer Correct Answer: A) $i$ $j$. 34. If A is a square matrix then AA' A) Is a skew symmetric matrix. B) Is not defined. C) =-AA'. D) Is a symmetric matrix. Show Answer Correct Answer: D) Is a symmetric matrix. 35. If all diagonal elements of a square matrix A are zero then A) Never a skew symmetric matrix. B) A is a skew symmetric matrix. C) A is a symmetric matrix. D) A may or may not be skew symmetric matrix. Show Answer Correct Answer: D) A may or may not be skew symmetric matrix. 36. If 0 is an eigenvalue of a matrix A, then A$^{2}$ is singular(singular means not invertible that is determinant is zero) A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 37. If A is an invertible matrix of order 3x3 and IAI=9. Then find IadjAI= A) 81. B) 9. C) 729. D) 18. Show Answer Correct Answer: A) 81. 38. 7). If a square matrix A has two identical rows or columns, then det.A is: A) 0. B) -1. C) 1. D) None of these. Show Answer Correct Answer: A) 0. 39. If for two matrices A and B, AB = 0, then A) A = 0 or B = 0. B) Both are O. C) None of them may be O. D) None of these. Show Answer Correct Answer: C) None of them may be O. 40. If P and Q are two different matrices of order 3 $\times$ $\times$ A) 3 $\times$. B) 3 $\times$. C) 4 $\times$. D) 4 $\times$. Show Answer Correct Answer: C) 4 $\times$. 41. Las Matriz Identidad es aquella: A) Que la diagonal secundaria es 1 y el resto de la matriz esta conformado por valores nulos. B) Que la diagonal secundaria es 2 y el resto d ela matriz esta conformado por valores nulos. C) Que la diagonal principal es 1 y el resto de la matriz esta conformado por valores nulos. D) Que la diagonal principal es 1 y el resto de la matriz esta conformado por cuanquier valor. Show Answer Correct Answer: C) Que la diagonal principal es 1 y el resto de la matriz esta conformado por valores nulos. 42. Es aquella matriz cuadrada en donde todos los elementos por debajo de la diagonal principal son nulos o ceros. A) Matriz Triangular Superior. B) Matriz Triangular Inferior. C) All the above. D) None of the above. Show Answer Correct Answer: A) Matriz Triangular Superior. 43. How would a scalar multiplication be carried out for a matrix? A) Subtract the elements in the first matrix from the elements of the second matrix. B) Add the Scalar to every element in the matrix. C) Multiply every element with the scalar to create a new matrix. D) Dot product the rows of one matrix with the columns of the other matrix. Show Answer Correct Answer: C) Multiply every element with the scalar to create a new matrix. 44. If m is a 7 x 5 matrix of rank 3 and N is a 5 x 7 matrix of rank 5, then rank (mn) is A) 3. B) 2. C) 1. D) 5. Show Answer Correct Answer: A) 3. 45. If A is a symmetric matrix and n $\epsilon$ $A^n$ A) Symmetric. B) Skew Symmetric. C) Diagonal. D) None of these. Show Answer Correct Answer: A) Symmetric. 46. (kA)'= (where k is any scalar) A) KA'. B) -kA'. C) -kA. D) $\frac{1}{k}A'$. Show Answer Correct Answer: A) KA'. 47. Para sumar dos matrices ..... A) Tienen que tener el mismo orden. B) No importa el orden de las matrices. C) Tienen que tener diferente orden. D) None of the above. Show Answer Correct Answer: A) Tienen que tener el mismo orden. 48. Element a32 is belongs to which row and column in a given matrix A. A) 2nd row, 3rd column. B) 3rd row, 2nd column. C) Can't decide. D) None of the above. Show Answer Correct Answer: B) 3rd row, 2nd column. 49. (k + l) A> kA + lA, where k and l are constant. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 50. The multiplicative inverse of matrix A is denoted by: A) A$^{t}$. B) |A|. C) Adj A. D) A$^{-1}$. Show Answer Correct Answer: D) A$^{-1}$. 51. If a matrix has equal number of rows and column, then it is called: A) Equal matrix. B) Rectangular matrix. C) Null matrix. D) Square matrix. Show Answer Correct Answer: D) Square matrix. 52. What would be the dimension of the matrix product AB?If A$_{1X4 }$and B$_{4X7}$ A) 7X1. B) 4X7. C) 1X7. D) 4X4. Show Answer Correct Answer: C) 1X7. 53. The rank of zero matrix is ..... A) Zero. B) One. C) Three. D) Two. Show Answer Correct Answer: A) Zero. 54. The adjoint of matrix A is denoted by: A) Adj A. B) |A|. C) A$^{t}$. D) A$^{-1}$. Show Answer Correct Answer: A) Adj A. 55. Which of the following statements is true regarding the eigenvalues of a diagonal matrix? A) The eigenvalues are always zero. B) The eigenvalues are the sum of the diagonal entries. C) The eigenvalues are the entries on the diagonal. D) The eigenvalues are the product of the diagonal entries. Show Answer Correct Answer: C) The eigenvalues are the entries on the diagonal. 56. El elemento a$_{42 }$de una matriz representa: A) Segunda columna y cuarta fila. B) Fila 2 y columna 4. C) Fila y columna igual. D) Segunda entrada. Show Answer Correct Answer: A) Segunda columna y cuarta fila. 57. Every square matrix can be uniquely expressed as sum of a symmetric and skew symmetric matrix. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 58. *For a system of n linear homogeneous equations to be have non-trivial solution must have A) *No condition on |A|. B) *|A| must be equal to zero. C) *|A| must be positive. D) |A| must be negative. Show Answer Correct Answer: B) *|A| must be equal to zero. 59. If A and B are square matrix of same order and B is a skew symmetric matrix then the matrix ABA' is A) Symmetric matrix. B) Skew symmetric matrix. C) May be symmetric may be skew symmetric. D) Not a square matrix. Show Answer Correct Answer: B) Skew symmetric matrix. 60. 8). Matrix A when multiplied with Matrix C gives the Identity matrix I, what is C? A) Inverse of A. B) Identity matrix. C) Transpose of A. D) Square of A. Show Answer Correct Answer: A) Inverse of A. ← PreviousNext →Related QuizzesScience QuizzesClass 12 QuizzesClass 12 Mathematics Chapter 3 Matrices Quiz 1Class 12 Mathematics Chapter 3 Matrices Quiz 2Class 12 Mathematics Chapter 3 Matrices Quiz 3Class 12 Mathematics Chapter 3 Matrices Quiz 4Class 12 Mathematics Chapter 3 Matrices Quiz 6Class 12 Mathematics Chapter 3 Matrices Quiz 7Class 12 Mathematics Chapter 1 Relations And Functions QuizClass 12 Mathematics Chapter 10 Vector Algebra Quiz 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books