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Engineering Maths - Linear Algebra

Avatto > > GATE COMPUTER SCIENCE > > Practice Questions > > Engineering Maths > > Linear Algebra

11. If AT = A^-1, where A is a real matrix, then A is

A
normal
B
symmetric
C
Hermitian
D
orthogonal

Answer
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Option : D
Explanation :

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12. If A and B are non-zero square matrices, then AB = 0 implies

A
A and B are orthogonal
B
A and B are singular
C
B is singular
D
A is singular

Answer
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Option : A
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13. If A and B be real symmetric matrices of size n x n, then

A
AA^T = 1
B
A = A^-1
C
AB = BA
D
(AB)^T = BA

Answer
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Option : D
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14. If, A, B, C are square matrices of the same order, then (ABC)^-1 is equal to

A
C^-1A^-1B^-1
B
C^-1 B^-1 A^-1
C
A^-1 B^-1C^-1
D
A^-1 C^-1 B^-1

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Option : B
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15. Consider the following statements

S1: Sum of the two singular n x n matrices may be non-singular

S2 : Sum of two the non-singular nx n matrices may be singular. Which of the following statements is correct?

A
S1 and S2 are both true
B
S1 is true, S2 is false
C
S1 is false, S2 is true
D
S1 and S2 are both false

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Option : A
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