Note : We have tried upload as much as we can, all the question and answers might be shuffled - Answers are marked in green. Thanks for Murthy,Abirami who helped us on this quiz.
Questions:
Select one:
A. Linearly dependent
B. Every linear combination is zero
C. Linearly Independent
D. Forms a basis for R^3
The correct answer: Linearly dependent
2.
A. 45
B. 0
C. 10
D. 3
The correct answer: 0
3. The elements along principal diagonal of a Hermitian matrix are all
Select one:
A. either zero or purely imaginary
B. real
C. 0
D. imaginary
A. either zero or purely imaginary
B. real
C. 0
D. imaginary
The correct answer: real
4. For the linearly dependent vectors X=[3,-9,12] and Y=[-4,12,-16]:
Select one:
A. X-2Y=0
B. 4X+3Y=0
C. 4X-3Y=0
D. 3X+4Y=0
A. X-2Y=0
B. 4X+3Y=0
C. 4X-3Y=0
D. 3X+4Y=0
The correct answer: 4X+3Y=0
5. If A and B are two orthogonal matrices, each of order n then AB and BA are
Select one:
A. Orthogonal
B. asymmetric
C. symmetric
D. Hermitian
The correct answer: asymmetric
6. A set of single non-zero vector is
Select one:
A. Basis
B. None
C. Linearly dependent
D. Linearly Independent
A. Basis
B. None
C. Linearly dependent
D. Linearly Independent
The correct answer: Linearly Independent
7.Which one of the following is false :
Select one:
A. Matrices is an arrangement while determinant is a value of square matrices.
B. If Rank of A= Rank of B
C. Row equivalent matrices have the same rank.
D. A linearly independent set in v consisting on a maximum possible no of vectors in V is called a basis for V
A. Matrices is an arrangement while determinant is a value of square matrices.
B. If Rank of A= Rank of B
C. Row equivalent matrices have the same rank.
D. A linearly independent set in v consisting on a maximum possible no of vectors in V is called a basis for V
The correct answer: If Rank of A= Rank of B
8. The Gauss-Elimination method, the augmented matrix reduces to…..................matrix
Select one:
a. Upper triangular
b. Diagonal
c. unit
d. None of these
a. Upper triangular
b. Diagonal
c. unit
d. None of these
The correct answer: Upper triangular
9. The Characteristics roots of an orthogonal matrix are of ------ modulus
Select one:
A. UnitB. Two
C. Three
D. Zero
The correct answer: Unit
10.Which of the following is not a elementary transformation?
Select one:
a. Adding two rows b. Squaring all the elements of the matrix
c. Adding two columns
d. Multiplying a row by a non-zero number
The correct answer: Squaring all the elements of the matrix
11.
A.
B.
C.
D.
12. If rank = number of unknowns and x = y = z = 0 the equation have only -------- solution
A. Non trivial
B. Infinite
C. Unique
D. Trivial
The correct answer: Trivial
13.
A. 3
B. 9
C. 1
D. -3
The correct answer: 3
14.If r is the rank of the matrix [A] of order m x n then r is
A. r is less than or equal to minimum of (m, n)
B. r is greater than or equal to 'm'
C. r is greater than 'n'
D. r is less than or equal to 'n'
The correct answer: r is less than or equal to 'n'
15. The standard basis of an inner product space R x R x R (R) forms an
A. Orthonormal set
B. Orthogonal set and Orthonormal set
C. Orthogonal set
D. Neither Orthogonal set nor Orthonormal set
The correct answer: Orthogonal set and Orthonormal set
16. Let A be a matrix having rank ‘r ' & B be the equivalent matrix obtained from A. Then rank of matrix B is…
Select one:
A. r + 2B. r -1
C. r
D. r + 1
The correct answer: r
17. State : which one is false :
Select one:
A. If A and B are Hermitian: then AB-BA is skew HermitianB.
C. If A is a skew Hermitian : then iA is Hermitian
D.
The correct answer: D
18.
Select one:
A. 6,6 B. 6,-12
C. 12,6
D. -6,12.
The correct answer: 6,-12
19. The linear transformation Y = AX is regular if
Select one:
A. I A I#0B. I A I=1
C. I A I=-1
D. I A I=0
The correct answer: I A I#0
20. A square matrix A of order 3 has 3 linearly independent Eigen vectors then a matrix P can be found such that P-1AP is a
A. Diagonal Matrix
B. Symmetric matrix
C. Singular matrix
D. Unit matrix
The correct answer: Diagonal Matrix