This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 3 Matrices – Quiz 6 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 3 Matrices Quiz 6 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. If B is a non-singular matrix and A is a square matrix, then det(B$^{-1}$AB) is equal to A) Det (A$^{-1}$). B) Det (A). C) Det (BAB). D) Det (B$^{-1}$). Show Answer Correct Answer: B) Det (A). 2. Factorise x$^{3}$ + 6x$^{2}$ + 11x + 6 completely using factor theorem. A) (x + 1) ( x + 2) ( x-3). B) (x + 1) ( x + 2) ( x + 3). C) (x + 1) ( x-2) ( x + 3). D) (x-1) ( x + 2) ( x + 3). Show Answer Correct Answer: B) (x + 1) ( x + 2) ( x + 3). 3. In matrices (AB)$^{t}$ equals to A) B$^{t}$ A$^{t}$. B) AB. C) BA. D) A$^{t}$ B$^{t}$. Show Answer Correct Answer: A) B$^{t}$ A$^{t}$. 4. To reduce a matric into normal form of the matrix, one can use ..... transformation. A) Row only. B) Column only. C) Both Row and Column. D) Both row or column or both. Show Answer Correct Answer: D) Both row or column or both. 5. Inverse of a square matrix, if it exists, is unique. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 6. If A and B are square matrices of equal degree, then which one is correct among the following? A) A-B = B-A. B) AB = BA. C) A + B = A-B. D) A + B = B +A. Show Answer Correct Answer: D) A + B = B +A. 7. How do we label a matrix? A) Column x Row. B) Row x Column. C) All the above. D) None of the above. Show Answer Correct Answer: B) Row x Column. 8. The determinant of unit matrix is A) 0. B) 1. C) Equal to its order. D) None of the above. Show Answer Correct Answer: B) 1. 9. If in a set of vectors any vector of the set is the linear combination of the remaining vectors, then the vectors are A) Linearly independent. B) Linearly dependent. C) Data inadequate. D) None of the above. Show Answer Correct Answer: B) Linearly dependent. 10. The slope of the straight line:3x-5y + 9 = 0 is A) -3/5. B) 5/3. C) 3/5. D) -5/3. Show Answer Correct Answer: C) 3/5. 11. What is the cofactor of the element in the first row and second column of a determinant? A) (-1)M, where M is the minor of the element. B) (-1)M, where M is the sum of the elements in the first row and second column. C) (-1)M, where M is the product of the elements in the first row and second column. D) (-1)M, where M is the square of the element. Show Answer Correct Answer: A) (-1)M, where M is the minor of the element. 12. If a matrix A has an eigenvalue of zero, what can be inferred about the matrix A? A) A is singular. B) A must be diagonal. C) A is invertible. D) A has full rank. Show Answer Correct Answer: A) A is singular. 13. Solve the system of equations using an inverse matrix:2x + 3y = 7 and 4x + y = 9. A) The solution is x = 2 and y = 1. B) The solution is x = 1 and y = 2. C) The solution is x = 3 and y = 1. D) The solution is x = 1 and y = 1. Show Answer Correct Answer: A) The solution is x = 2 and y = 1. 14. Integral of Cot 6x = A) (log Sin 6x)/6. B) -(log Sin 6x)/6. C) (log Cos 6x)/6. D) -(log Cos 6x)/6. Show Answer Correct Answer: A) (log Sin 6x)/6. 15. The Element $a_{23}$ A) In the second Row and third Column. B) In the third Row and second Column. C) In the second Column and third Row. D) None of the above. Show Answer Correct Answer: A) In the second Row and third Column. 16. For any Square Matrix, A + $A^T$ A) Symmetric. B) Skew-Symmetric. C) NULL mATRIX. D) NONE OF THESE. Show Answer Correct Answer: A) Symmetric. 17. Perform the multiplication of the matrices [[1, 2], [3, 4]] and [[0, 1], [1, 0]]. A) [[2, 1], [4, 3]]. B) [[1, 0], [2, 3]]. C) [[0, 2], [4, 1]]. D) [[3, 4], [1, 2]]. Show Answer Correct Answer: A) [[2, 1], [4, 3]]. 18. If the points A(3, -2), B(k, 2) and C(8, 8) are collinear, then the value of k is: A) -4. B) -3. C) 5. D) 2. Show Answer Correct Answer: C) 5. 19. If $\lambda$ is an eigenvalue of matrix A, then linear system (A-$\lambda$I)v=0 has only trivial solution. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 20. Classify the matrix [[1, 2, 3], [0, 0, 0]] by its type. A) Diagonal matrix (non-deficient). B) Identity matrix (rank-deficient). C) Rectangular matrix (rank-deficient). D) Square matrix (full rank). Show Answer Correct Answer: C) Rectangular matrix (rank-deficient). 21. If the matrix AB is zero, then A) It is not necessary that either A = O or B = O. B) A = O or B = 0. C) A = O and B = O. D) All the above statements are wrong. Show Answer Correct Answer: A) It is not necessary that either A = O or B = O. 22. Para obtener la transpuesta de una matriz se tiene que A) Cambiar las filas por las columnas. B) Ninguna. C) Cambiar el signo de los elementos de la matriz. D) Las dos anteriores. Show Answer Correct Answer: A) Cambiar las filas por las columnas. 23. Null Matrix has determinant of (a) A) A. 0. B) 1. C) None. D) None of the above. Show Answer Correct Answer: A) A. 0. 24. La matriz traspuesta de la traspuesta de A es: A) La matriz identidad. B) La matriz nula. C) La matriz adjunta. D) La matriz A. Show Answer Correct Answer: D) La matriz A. 25. Solve the system for the value of y:2y + 7x + 6 =-132y-x-7 = 14 A) Y =-8. B) X =-5. C) Y =-5. D) Y = 8. Show Answer Correct Answer: D) Y = 8. 26. Transpose of an orthogonal matrix is ..... A) Symmetric. B) Skew symmetric. C) Hermitian. D) Orthogonal. Show Answer Correct Answer: D) Orthogonal. 27. Solve the following system using an augmented matrix. Use your calculator.-3x + y = 4-5x + 2y-4z =-3-x-4y-6z = 11 A) (2, -3, -5). B) (2, -5, -3). C) (2, -4, -4). D) (-3, -5, 2). Show Answer Correct Answer: D) (-3, -5, 2). 28. Solve the system of equations using matrices:3x + 2y-z = 11, 2x-y + 3z = 4, and x + 3y-2z = 9. A) The solution for the system of equations is x = 3, y = 2, and z = 1. B) The solution for the system of equations is x = 3, y = 1, and z = 2. C) The solution for the system of equations is x = 2, y = 3, and z = 1. D) The solution for the system of equations is x = 1, y = 3, and z = 2. Show Answer Correct Answer: C) The solution for the system of equations is x = 2, y = 3, and z = 1. 29. We can calculate determinants of which matrices A) All matrices. B) All matrices except square matrices. C) All matrices except rectangular matrices. D) Only square matrices. Show Answer Correct Answer: D) Only square matrices. 30. Calculate the product of the matrices [[1, 2], [3, 4]] and [[5], [6]]. A) [[10], [24]]. B) [[20], [30]]. C) [[17], [39]]. D) [[15], [35]]. Show Answer Correct Answer: C) [[17], [39]]. 31. If A is $3\times4$ A) $3\times3$. B) $3\times4$. C) 4 $\times$. D) $4\times4$. Show Answer Correct Answer: A) $3\times3$. 32. If A and B are nonsingular matrices of the same order then (adj AB) = A) (adj A)(adj B). B) (adj B)(adj A). C) Does not exist. D) None of these. Show Answer Correct Answer: B) (adj B)(adj A). 33. What is the condition for two matrices to get multiplied? A) They must be square. B) There order must be equal always. C) No. of COLUMNS of first matrix should be equal to No. of ROWS of second matrix. D) None of these. Show Answer Correct Answer: C) No. of COLUMNS of first matrix should be equal to No. of ROWS of second matrix. 34. Which one comes first in the order of a matrix? A) Row. B) Column. C) All the above. D) None of the above. Show Answer Correct Answer: A) Row. 35. 14). If A and B are matrices of the same order, then (AB'-BA') is a A) Null matrix. B) Symmetric matrix. C) Unit matrix. D) Skew-symmetric matrix. Show Answer Correct Answer: D) Skew-symmetric matrix. 36. In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from both the numerator and denominator, the fraction is decreased by 1/14. Find the fraction. A) 4/7. B) -9/-6. C) 3/2. D) 3/7. Show Answer Correct Answer: A) 4/7. 37. Dada el orden de cada matriz A = 3x2B= 2x1la matriz resultante de AxB es A) 2 filas x 2 columnas. B) 3 filas x 1 columna. C) No se puede realizar la operacion. D) None of the above. Show Answer Correct Answer: B) 3 filas x 1 columna. 38. What is the area of triangle XYZ with vertices X(8, -6), Y(-4, 2) and Z(-18, -12)? A) 280. B) 140. C) 240. D) 180. Show Answer Correct Answer: B) 140. 39. A singular matrix has its determinant zero. True or False? A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 40. The polynomials 2x$^{3}$-7x$^{2}$ + ax-6 and x$^{3}$-8x$^{2}$ + (2a + 1)x-16 leaves the same remainder when divided by x-2. Find the value of 'a'. A) A = 10. B) A = 30. C) A = 20. D) A = 40. Show Answer Correct Answer: A) A = 10. 41. If a system has infinite solutions, then it means: A) The lines or planes don't intersect. B) The lines or planes are parallel. C) The lines or planes intersect at a line. D) You get 0=some number when solving the system. Show Answer Correct Answer: C) The lines or planes intersect at a line. 42. (3 X 4) Matrix have: A) 7 Elements. B) 4 Elements. C) 12 Elements. D) 3 Elements. Show Answer Correct Answer: C) 12 Elements. 43. What is the order of a matrix?(HINT:How are dimensions of a matrix written?) A) Number of elements. B) Number of diagonals. C) Number of rows and columns. D) Number of columns and rows. Show Answer Correct Answer: C) Number of rows and columns. 44. What property of matrices states that the product of a matrix and the identity matrix is the matrix itself? A) Distributive Property of Matrix Multiplication. B) Identity Property of Matrix Multiplication. C) Commutative Property of Matrix Addition. D) Associative Property of Matrix Multiplication. Show Answer Correct Answer: B) Identity Property of Matrix Multiplication. 45. The transpose of matrix A is denoted by: A) |A|. B) Adj A. C) A$^{t}$. D) A$^{-1}$. Show Answer Correct Answer: C) A$^{t}$. 46. A diagonal matrix, all of whose diagonal elements are equal, is called: A) Diagonal matrix. B) Scalar matrix. C) Unit matrix. D) Null matrix. Show Answer Correct Answer: B) Scalar matrix. 47. Matrices can be used to A) Store information. B) Solve sets of simultaneous equations. C) Analyse networks. D) Encode information. E) All of the above. Show Answer Correct Answer: E) All of the above. 48. What is the property of a matrix that states A + B = B + A? A) Distributive property of multiplication. B) Associative property of addition. C) Identity property of addition. D) Commutative property of addition. Show Answer Correct Answer: D) Commutative property of addition. 49. Matrix A = 2 x 7, matrix B = 7 x 2 Determine which of the following operations exist. A) AB$^{t}$. B) BA. C) A + B. D) AB. Show Answer Correct Answer: B) BA. 50. Matrices are denoted by? A) Letters. B) Numbers. C) Shapes. D) All of the above. Show Answer Correct Answer: A) Letters. 51. Que es una matriz triangular superior. A) Es una matriz cuadrada en donde todos sus elementos situados por encima de la diagonal principal son cero. B) Es una matriz rectangular en donde todos sus elementos situados por debajo de la diagonal son cero. C) Es una matriz cuadrada en donde todos sus elementos situados por debajo de la diagonal principal son cero. D) Es una matriz 2x3 en donde todos sus elementos situados por debajo de la diagonal son cero. Show Answer Correct Answer: C) Es una matriz cuadrada en donde todos sus elementos situados por debajo de la diagonal principal son cero. 52. Si $A$ $B$ $\left(AB\right)^{-1}=A^{-1}B^{-1}$ A) Verdadero. B) Falso. C) All the above. D) None of the above. Show Answer Correct Answer: B) Falso. 53. The eigenvalue of a real symmetric matrix is A) Real. B) Imaginary. C) Zero. D) None. Show Answer Correct Answer: A) Real. 54. Una matriz diagonal se define como ..... A) Si los elementos de la diagonal principal son iguales a 1. B) Si los elementos de la diagonal principal son iguales. C) Si todos los elementos de encima y debajo de la diagonal principal son 0. D) Si los elementos situados por encima de la diagonal son 0. Show Answer Correct Answer: C) Si todos los elementos de encima y debajo de la diagonal principal son 0. 55. Una matriz fila es aquella que solo tiene una fila A) Verdadera. B) Falso. C) All the above. D) None of the above. Show Answer Correct Answer: A) Verdadera. 56. Si una matriz es de orden 3x2 el rango maximo que puede tener es A) 3. B) 2. C) Ninguna de las anteriores. D) None of the above. Show Answer Correct Answer: B) 2. 57. A diagonal matrix is said to be a scalar matrix if its diagonal elements are not equal, A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 58. Eigenvalue of a square matrix A are roots of differential equation A) Characteristic equation. B) Integral equation. C) Logical equation. D) None of the above. Show Answer Correct Answer: A) Characteristic equation. 59. Classify the matrix [[1, 0], [0, 1]] by its type. A) Identity matrix. B) Diagonal matrix. C) Zero matrix. D) Symmetric matrix. Show Answer Correct Answer: A) Identity matrix. 60. Integral of x$^{-5/3}$ = A) (-3/2) x$^{-2/3}$. B) (5/3) x$^{-2/3}$. C) (-3/8) x$^{-8/3}$. D) (-5/3) x$^{-8/3}$. Show Answer Correct Answer: A) (-3/2) x$^{-2/3}$. ← 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 5Class 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