## June 12, 2019

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:

1. In R^3   the four vectors (1,2,5)  (5,9,3) (329,431,731) and (21, -13,58) are
Select one:
A. Linearly dependent
B. Every linear combination is zero
C. Linearly Independent
D. Forms a basis for R^3

2.

Select one:
A. 45
B. 0
C. 10
D. 3

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

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

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

6. A set of single non-zero vector is

Select one:
A. Basis
B. None
C. Linearly dependent
D. 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

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

9. The Characteristics roots of an orthogonal matrix are of ------ modulus

Select one:
A. Unit
B. Two
C. Three
D. Zero

10.Which of the following is not a elementary transformation?

Select one:
b. Squaring all the elements of the matrix
d. Multiplying a row by a non-zero number

The correct answer: Squaring all the elements of the matrix

11.

Select one:
A.

B.

C.

D.

12. If  rank = number of unknowns  and x = y = z = 0 the equation have only -------- solution

Select one:
A. Non trivial
B. Infinite
C. Unique
D. Trivial

13.

Select one:
A. 3
B. 9
C. 1
D. -3

14.If r is the rank of the matrix [A] of order m x n then r is

Select one:
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

Select one:
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 + 2
B. r -1
C. r
D. r + 1

17. State : which one is false :
Select one:
A. If A and B are Hermitian: then AB-BA is skew Hermitian

B.

C. If A  is a  skew Hermitian : then iA  is Hermitian

D.

18.

Select one:
A. 6,6
B. 6,-12
C. 12,6
D. -6,12.

19. The linear transformation Y = AX is regular if

Select one:
A. I A I#0
B. 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

Select one:
A. Diagonal Matrix
B. Symmetric matrix
C. Singular matrix
D. Unit matrix

1. Huge respect guys... You're doing great...

2. Please update the corrected answers after evaluating the quiz from BITS, so it may helpful fr others.

15) The standard basis of an inner product space R x R x R (R) forms an

Select one:
A. Orthogonal set
B. Orthogonal set and Orthonormal set
C. Neither Orthogonal set nor Orthonormal set
D. Orthonormal set Incorrect
Feedback
The correct answer is: Orthogonal set and Orthonormal set

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

Select one:
A. Diagonal Matrix
B. Singular matrix
C. Unit matrix
D. Symmetric matrix Incorrect
Feedback
The correct answer is: Diagonal Matrix

14)If r is the rank of the matrix [A] of order m x n then r is

Select one:
A. r is greater than or equal to 'm'
B. r is less than or equal to minimum of (m, n) Incorrect
C. r is less than or equal to 'n'
D. r is greater than 'n'
Feedback
The correct answer is: r is less than or equal to 'n'

5)If A and B are two orthogonal matrices, each of order n then AB and BA are

Select one:
A. Orthogonal Incorrect
B. Hermitian
C. symmetric
D. asymmetric
Feedback

19)The linear transformation Y = AX is regular if

Select one:
A. I A I=-1
B. I A I=1 Incorrect
C. I A I=0
D. I A I#0
Feedback
The correct answer is: I A I#0The linear transformation Y = AX is regular if

Select one:
A. I A I=-1
B. I A I=1 Incorrect
C. I A I=0
D. I A I#0
Feedback
The correct answer is: I A I#0

Thanks for the help

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We appreciate your help. it would be better if from now onwards, you send answers through submit question and answer tab so it would be easy for us to update on Waseian. :)