Matrices Test

Result

Matrices Test - 6

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Weekly Quiz Competition

Question 1
1 / -0

Adj.(KA) = ….

A
K^n-1 Adj. A

B
K Adj. A

C
KⁿAdj.A

D
None of these

Solution

Adj. (KA) = K^n-1 Adj.A, where K is a scalar and A is a n × n matrix.
Question 2
1 / -0

If A and B are any two square matrices of the same order, then

A
(AB)^t = A^tB^t

B
adj(AB) = adj(A) adj (B)

C
AB = O

D
(AB)^t = B^tA^t

Solution

By the property of transpose ,(AB )’ = B’A’
Question 3
1 / -0

If A is any square matrix, then

A
A + A^t is symmetric

B
A - A^t is symmetric

C
A + A^t is skew-symmetric

D
none of these

Solution

For every square matrix (A + A’ ) is always symmetric.
Question 4
1 / -0

If A is any square matrix then which of the following is not symmetric ?

A
AA^t

B
A - A^t

C
A+A^t

D
A^tA

Solution

For every square matrix (A – A’ ) is always skew – symmetric.
Question 5
1 / -0

Each diagonal element of a skew-symmetric matrix is

A
Positive

B
negative

C
Zero

D
non-real

Solution

The diagonal elements of a skew-symmetric matrix is zero.

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Matrices Test - 6

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Matrices Test - 6

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Question 1

Kn-1 Adj. A

K Adj. A

Kn Adj.A

None of these

Solution

Question 2

(AB)t = AtBt

adj(AB) = adj(A) adj (B)

AB = O

(AB)t = BtAt

Solution

Question 3

A + At is symmetric

A - At is symmetric

A + At is skew-symmetric

none of these

Solution

Question 4

AAt

A - At

A+At

AtA

Solution

Question 5

Positive

negative

Zero

non-real

Solution

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K^n-1 Adj. A

KⁿAdj.A

(AB)^t = A^tB^t

(AB)^t = B^tA^t

A + A^t is symmetric

A - A^t is symmetric

A + A^t is skew-symmetric

AA^t

A - A^t

A+A^t

A^tA