BSC II Algebra I(Matrices)

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1) The diagonal elements of Hermitian matrix are -------

1 point

real

imaginary

zero

none of these

Clear selection

2) The necessary and sufficient condition for a matrix A to be Hermitian is that ------

1 point

A = A^θ

A =-A^θ

A is zero matrix

none of these

Clear selection

3) If A and B are Skew-Hermitian matrices, then A+B is ------

1 point

Hermitian

Skew-Hermitian

c) symmetric

Skew-symmetric

Clear selection

4) If A is a Skew-Hermitian matrix, then iA is -------

1 point

Hermitian

Skew-Hermitian

symmetric

Skew-symmetric

Clear selection

5) If the system of equations has one or more solutions then the equations are ---------

1 point

Inconsistent

consistent

Homogeneous

Non-Homogeneous

Clear selection

6) The system of equations AX = B is consistent if and only if ------

1 point

ρ(A)= ρ([A∶B])

ρ(A)< ρ([A∶B])

ρ(A)> ρ([A∶B])

none of these

Clear selection

7) The set of all eigen values of a matrix A is called ------

1 point

The spectrum of A

eigen vectors of A

characteristic vectors of A

none of these

Clear selection

8) The product of eigen values of a matrix A is -------

1 point

Not equal to the determinant of A

Equal to the determinant of A

none of these

Clear selection

9) The rank of a null matrix is --------

1 point

∞

Clear selection

10) Any square matrix and its transpose have -------

1 point

All eigen values zero

The different eigen values

The same eigen values

none of these

Clear selection

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