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Engineering Maths - Linear Algebra Online Exam Quiz

Important questions about Engineering Maths - Linear Algebra. Engineering Maths - Linear Algebra MCQ questions with answers. Engineering Maths - Linear Algebra exam questions and answers for students and interviews.

1. Rank of the matrix A =

Options

A : 0

B : 1

C : 2

D : 3

2. A set of linear equations is represented by the matrix equation Ax = b. The necessary condition for the existence of a solution for this system is

Options

A : A must be invertible

B : b must be linearly depended on the columns of A

C : b must be linearly independent of the columns of A

D : None of these

3. The system of linear equations                                                           (4d - 1)x +y + z = 0                                                                                 - y + z = 0                                                                                             (4d - 1) z = 0                                                                                             has a non-trivial solution, if d equals

Options

A : 1/2

B : 1/4

C : 3/4

D : 1

4. The rank of a 3 x 3 matrix C (= AB), found by multiplying a non-zero column matrix A of size 3 x 1 and a non-zero row matrix B of size 1 x 3, is

Options

A : 0

B : 1

C : 2

D : 3

5. If A and B are square matrices of size n x n, then which of the following statement is not true?

Options

A : det. (AB) = det (A) det (B)

B : det (kA) = k n det (A)

C : det (A + B) = det (A) + det (B)

D : det (A T ) =1/det (A -1 )

46. An arbitary vector X is an eigen vector of the matrix

Options

A : (0,0)

B : (1,1)

C : (0,1)

D : (1,2)

47. For which value of k, the following system is consistent?

Options

A : 1

B : 2

C : 3

D : 5

48. The value of  λ for which the equations

Options

A : 2

B : 4

C : 6

D : 8

49. The system of equations

Options

A : a 1 b 1 = a 2 b 2

B : a 1 b 2 = a 2 b 1

C : a 1 a 2 = b 1 b 2

D : none of these

50. The solution of the given matrix equation is

Options

A : x 1 =0, x 2 =0, x 3 =0

B : x 1 =1, x 2 =1, x 3 =0

C : x 1 =0, x 2 =1, x 3 =1

D : x 1 =2, x 2 =-5, x 3 =-1

51. If product of matrix

Options

A : odd multiple of π

B : even multiple of π

C : odd multiple of π/2

D : even multiple of π/2

52. Sum of the eigen values of the matrix

Options

A : greater than zero

B : less than zero

C : zero

D : dependent on value of x

53. The system of equations

Options

A : no solutions

B : only one solution

C : two solutions

D : infinite number of solutions

54. The system of equations

Options

A : no solutions

B : only one solution

C : two solutions

D : infinite number of solutions

55. Eigen values of

Options

A : 0,0,0

B : 0,0,1

C : 0,0,3

D : 1,1,1

56. If R=

Options

A : [5 6 4]

B : [5 -3 1]

C : [2 0 1]

D : [2 -1 1/2]

57. Sum of the eigen values of the matrix

Options

A : 5

B : 7

C : 9

D : 18

58. For which value of x, will the matrix

Options

A : 4

B : 6

C : 8

D : 12

59. Rank of the matrix,

Options

A : 1

B : 2

C : 3

D : none of these

60. Eigen vectors of the matrix

Options

A : (1,0)

B : (0,1)

C : (1,1)

D : (1,-1)

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