Matrices

The value of a _____ does not change when rows and columns are interchanged.

• matrix

• determinant

• linear space

• none of the above

Inverse of a square matrix is ____ if it exists

• different

• exists

• unique

• none of the above

If A be any square matrix,then AA' and A'A will be both

• Skew symmetric

• symmetric

• either skew symmetric or symmetric

• neither skew symmetric nor symmetric

Transpose of an orthogonal matrix is ______

• symmetric

• skew symmetric

• hermitian

• orthogonal

A square matrix A= $\left[a_{ij}\right]_{n\times n}$  is _______ iff  $\overline{a_{ij}}\ =a_{ji}$  

• skew hermitian

• symmetric

• skew symmetric

• hermitian

The rank of zero matrix is _______

• one

• two

• zero

• three

The rank of every non-singular matrix of order n is _____

• 1

• 0

• 2

• n

If A and B are two n-rowed square matrices, then  $\rho\left(AB\right)---\rho\left(A\right)+\rho\left(B\right)-n$  

•  $\ge$  

•  $\le$  

•  $\ne$  

• >

Let AX=B be a system of m linear equations in n variables.If |A|=0 and adj(A).B=0,then the system is __________

• consistent and has unique solution

• consistent and has infinite number of solutions

• inconsistent and has no solution

• none of the above

If in a set of vectors any vector of the set is the linear combination of the remaining vectors, then the vectors are

• linearly independent

• linearly dependent

• data inadequate

• none of the above