VU Midterm Past Papers
198 solved midterm past paper MCQs for MTH501 at Virtual University, each with the correct answer marked. Use them to learn the VU question style and test your recall. An independent study tool — not affiliated with VU.
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Q1. Whenever a solution set is described explicitly with vectors, we say that the solution is in parametric vector form. The equation x=su+tv (s, t in R) is called
Q2. If A = [[1,2],[3,2]] ~ [[1,0],[0,1]] then the columns of A are Linearly
Q3. If A and B are matrices then A+B is only possible if both matrices have same
Q4. If AB = I = BA for matrices A, B and I, where I is an identity matrix, then
Q5. Let W = {(x, y) such that x, y in R and y = 0}. Is W a vector subspace of plane?
Q6. The equation Ax = b has a solution if and only if
Q7. Which of the following would be the Augmented Matrix associated with the system: a - b = 1, 2a + b = 0?
Q8. A determinant does not change if we add a multiple of a row to another row.
Q9. How many assumptions are there in Jacobi's method?
Q10. Suppose k is any scalar and u = (u1,u2,...,un), v = (v1,v2,...,vn) in R^n, then the distributive law states that
Q11. An m x m matrix is only square matrix that is both unit lower triangular and upper triangular.
Q12. Why is [1 2] NOT possible?
Q13. If the equation: (4 1) (x) = (3) has the solution for all t in R, then (7) and (1) will span
Q14. Which of the following is corresponding Matrix form of the Linear equation x + y = 3?
Q15. According to determinant properties, the determinant of resulting matrix equals k times delta if elements of rows are
Q16. If a matrix A is invertible then adj(A) is also invertible.
Q17. If a matrix is in reduced row echelon form, then it is also in row echelon form.
Q18. While using Cramer's rule, if determinant D = 0 and other determinant is not zero then how many solutions are there?
Q19. A matrix has not the same determinant if we add a multiple of a column to another column.
Q20. Since vector (3) lies in the span of {(1),(2)} then the vectors (3), (5) and (1) are Linearly
Q21. If a square matrix A can be reduced to row echelon form with ____ interchanges, then A has an LU-decomposition.
Q22. A transformation T: R^n -> R^m is a rule that assigns to each vector x in R^n an image vector T(x) in R^m. The set R^n is called the ____ and R^m is called the ____.
Q23. Algebraic expression involving more than one term and less than 3 terms is known as
Q24. At what condition det(AB) = (detA)(detB) is possible?
Q25. Which of the following can refer a single term of an Algebraic expression?
Q26. Which of the following is an example of Matrix in Echelon form?
Q27. The Gauss-Seidel method is applicable to symmetric ____ definite matrices.
Q28. If the determinant of the matrix A is 32 and the matrix B is obtained by multiplying any row of A with an integer value 4, then which of the following is true for the matrix B?
Q29. Let V be a five-dimensional vector space, and let S be a subset of V which spans V. Then S
Q30. If λ is an eigenvector of A, then every nonzero vector x such that Ax = λx is called an ________ of A corresponding to ________.
Q31. If x + 2 is a factor of the characteristic polynomial of matrix C then an eigenvalue of C is
Q32. Let A be n × n matrix, then A is invertible if and only if
Q33. Gauss-Seidel method is also termed as a method of
Q34. If one of the eigenvalues of A is zero, it implies ___.
Q35. If u + v = u + w, then:
Q36. If the determinant of the matrix A is -1 and the matrix B is obtained by adding 2 times of the second row in the first row of the matrix A, then which of the following is true for the matrix B?
Q37. Which of the following will be the Matrix Product corresponding to Linear Combination: 2(-3,5) + 3(1,1)?
Q38. The solution of Ax = b exists if and only if b can be written as a linear combination of ________ of A.
Q39. A sufficient condition for the Jacobi's method to converge for the linear system Ax=b
Q40. Two simultaneous linear equations in two variables have no solution if their corresponding lines are ________.
Q41. Which of the following will be the Linear Combination corresponding to [[2,-3],[5,1]]*[x,y]?
Q42. If a homogeneous system Ax=0 has a trivial solution, then which of the following is (are) the value(s) of the vector x?
Q43. A square matrix A is said to be diagonal if A is similar to a matrix
Q44. Why inverse of the matrix A= [1 2] is NOT possible?
Q45. Which of the following Elementary Row operations would perform in order to get [[1,2,-5],[-4,1,-6],[6,3,-4]] ~ [[1,2,-5],[0,9,-36],[0,-9,26]]?
Q46. What is the maximum possible number of pivots in a 6 × 6 matrix?
Q47. A homogeneous linear system always has the trivial solution: there are only two possibilities for its solutions:
Q48. A system of linear equations is said to be homogeneous if the constant terms are all
Q49. In A is a square matrix, then the minor of entry ith row and jth column is to be the determinant of the sub matrix that remains when the ith row and jth column of A are
Q50. 7x is an algebraic term in which 7 is a ________ and x is a ________.
Q51. Which of the following is the coefficient matrix for the system: x1 - 2x2 + x3 = 0, 2x2 - 7x3 = 8, -4x1 + 3x2 + 9x3 = 3?
Q52. Let 'Ax = 0' be a homogeneous linear system of 'n' equations and 'n' unknowns. Then, the coefficient matrix 'A' is invertible if and only if this system has ________ solution.
Q53. If A be the standard matrix of linear transformation T: R^n -> R^m, then which of the following is true for the mapping from R^n onto R^m?
Q54. If T be a transformation, then which of the following is true for its linearity?
Q55. Which of the following is true for the matrix [[1,0,0],[0,2,0],[0,0,3]]?
Q56. 9x^2 + 3x + 4 is ________.
Q57. An n × n matrix A is said to be diagonalizable if and only if A has n ________ eigenvectors.
Q58. What is Eigen value?
Q59. Which of the following is true about the existence of free variables (parameter) in a system of linear equations?
Q60. If A = [[2,1],[4,3]] and B = [[1+1,2-1],[2+2,4-1]], then which of the following is true for A and B?
Q61. If Ax = b and factorization of A is LU, then which of the following pair of equations can be used to solve LUx = b for value of x?
Q62. A 3 × 3 identity matrix have three and ________ eigen values.
Q63. A system of linear equations is said to be homogeneous if it can be written in the form ________.
Q64. Let A be the matrix of order 2x3 and B be the matrix of order 3x5, and then which of the following is the order of the matrix AB?
Q65. How many Pivot partitions the matrix: [[2,3,1],[4,6,2]] will have?
Q66. If A = [[1,0,0],[0,1,0],[0,k,1]], then which of the following is true for the matrix?
Q67. If v1, v2, and v3 are in R^m then which of the following is equivalent to [2,7,-5]?
Q68. For any subspace W of a vector space V, which one is not the axiom for subspace.
Q69. Which one is not the axiom for vector space?
Q70. For any 3x3 matrix A where det (A) = 3, then det (2A) = ________.
Q71. If a multiple of one row of a square matrix A is added to another row to produce a matrix B, then which of the following condition is true?
Q72. While using the Cramer’s rule, if determinant D = 0, and other determinant is not zero then how many solutions are there?
Q73. Which of the following is all permutations of {1,2}?
Q74. At what condition the Cramer’s formula is valid for linear systems?
Q75. Which of the following is the volume of the parallelepiped determined by the columns of A where A is a 3 x 3 matrix?
Q76. Which of the following is NOT the axiom for vector space where u, v, w in V are set of vectors and l, m, n are scalars?
Q77. If two rows or columns of a square matrix are identical, then det (A) will be _______.
Q78. If A is strictly diagonally dominant, then A is _________.
Q79. If the absolute value of each diagonal entry exceeds the sum of the absolute values of the other entries in the same row then a matrix A is called:
Q80. If A is a triangular matrix, then det(A) is the product of the entries on the ________.
Q81. If all the entries of a row or a column of a square matrix are zero, then det (A) will be _____________.
Q82. Consider a system of linear equations Ax = b where A is a 3×3 matrix having 3 pivot positions, then which statement is false about the system Ax = b?
Q83. If rank of a 3 x 5 matrix is 3 then dimension of its Null space is
Q84. If matrix A has zero as an eigenvalue then which statement(s) about A must be true. I. Matrix A is not invertible. II. Matrix A will also have an eigenvalue 2. III. Matrix is diagonalizable.
Q85. Determinant of a non-invertible(singular) matrix always
Q86. Rank of a zero matrix of any order is
Q87. If a system of equations is solved using the Jacobi’s method, then which of the following is the most appropriate answer about the matrix M that is derived from the coefficient matrix?
Q88. If A is a square matrix, then the Minor of entry I th row and j th column is to be the determinant of the sub matrix that remains when the I th row and j th column of A are:
Q89. If M=[3] then which of the following is the determinant of the matrix M?
Q90. If M is a square matrix having two rows equal then which of the following about the determinant of the matrix is true?
Q91. If a system of equations is solved using the Gauss-Seidel method, then which of the following is the most appropriate answer about the matrix M that is derived from the coefficient matrix?
Q92. At what condition the Cramer’s rule fails?
Q93. Cramer’s rule is a formula for solving systems of equations by __________.
Q94. For an n×n matrix (At ) t =
Q95. What is the largest possible number of pivots a 4×6 matrix can have?
Q96. The characteristic polynomial of a 5×5 matrix is 543 4 45 , the eigenvalues are
Q97. A is diagonalizable if A =PDP-1 Where
Q98. The inverse of an invertible lower triangular matrix is
Q99. Let A be a n*m matrix of rank then row space of A has dimension
Q100. The dimension of the vector space p4 is
Q101. Let (3, 2), (4,5)uV .For the weighted Euclidean inner product 1 12 2 , 45 , u vu v u v u v -2
Q102. Let A be n*n matrix whose entries are real. If is an eigenvalue of A with X a corresponding eigenvector in Cn, then
Q103. Which one is the numerical method used for approximation of dominant eigenvalue of a matrix
Q104. The matrix equation represents a system of linear equations commonly referred to as the
Q105. Let have eigenvalues 2, 5, 0,-7, and -2. Then the dominant eigenvalue for A is
Q106. Which statement about the set S is false where S = {(1, 1, 3), (2, 3, 7),(2, 2, 6)}
Q107. How many subspaces R2 have?
Q108. The set of vectors {(5,0,0), (7,2,-6), (9,4,-8)} is,
Q109. is a 2 * 2 matrix, the area of the parallelogram determined by the columns of A is
Q110. transpose of an lower triangular matrix is
Q111. A be a square matrix of order 3 * 3 with det(A) =21 , then det(2 A ) =
Q112. A be an m × n matrix. If for each b in m ℝ the equation Ax=b has a solution then
Q113. equation x = p + t v describes a line
Q114. Given the system 123 23 123 28 2x 7 0 4 3 96 x x x x x x x the augmented matrix for the system is
Q115. a b c d e f g h i =5 then a b c 3d 3e 3f g h i will be
Q116. Each Linear Transformation T from Rn to Rm is equivalent to multiplication by a matrix A of order
Q117. Reduced echelon form of the matrix 12 3 2 3 4 is
Q118. The determinant of A is the product of the pivots in any echelon form U of A , multiplied by (-1)r , Where r is
Q119. Can add the matrices of ______________.
Q120. Solving system of equations with iterative method, we stop the process when the entries in two successive iterations are ________.
Showing the first 120 of 198 MCQs.