Matrix MCQ - 1 - Mathematics MCQ

All real

All imaginary

Equal

One real and the other imaginary

Two

Three

Four

None of these

-2

-1/2

0

2

None of these

-63

20

-43

None of these

2,7,11

7,11,2

11,2,7

7 ,2 ,11

(2, 2, 0) 

(0, 3, 2) 

(2, 2, 1) 

(2, –1, –2)

No solution 

Two solutions

Infinite many solution 

A unique solution 

A^T has rank n

A has n linearly independent columns

A is non — singular

A is singular

Possesses a trivial solution only

Possesses a unique non — trivial solution

Possesses finite number of non — trivial solution

Has infinitely many solution

Has a unique non — zero solution

Does not have any non — zero solution 

Has infinitely many non — zero solution

is inconsistent

Not Associative and Not commutative

Commutative but not associative 

Associative and commutative both

None of these

Trace of a unit matrix is always a fixed natural number

Trace of the sum of two matrices is equal to sum of their traces

Trace of the scalar matrix is some multiple of its order

T_r(AB) = T_r(BA)

(A + B)^T = A^T + B^T

(AB)^T = A^TB

(KA)^T = K^TA^T

none of the above

The transpose of a symmetric matrix need not be summetric matrix.

If A and B are symmetric matrix of same order, then AB + BA must be symmetric matrix.

If A is symmetric matrix, then all positive integral powers of A are symmetric matrices.

If A is any square matrix, then A + A'is always symmetric

If A is orthogonal matrix, then A is non — singular and A^-1= A'

If A is orthogonal matrix, then |A| = ± 1

Transpose of an orthogonal matrix is orthogonal

None of the above

If A is unitary matrix, then A'is also unitary matrix.

Inverse of unitary matrix is unitary matrix.

Inverse of unitary matrix is diagonal matrix.

None of these

In a Skew — Hermitian Matrix, the element of the principle diagonal must not be purely imaginary.

If A is Hermitian Matrix, then iA is Skew — Hermitian Matrix.

If A is any square matrix, then A — A^θ is Skew — Hermitian Matrix.

All of the above

The eigen values of a real symmetric matrix are all real

The modulus of each eigen value of a unitary matrix is unity

The eigen value of a Skew — Hermitian Matrix is either zero or a pure imaginary number

 None of these