Matrix

If X=[a_ij], i≥1, j≤n, with a_ij=i·j
Then number of linearly independent Rows are:

Which of the following is not correct?
(A) If A, B are two matrices such that AB = A and BA=B, then A and B are idempotent.
(B) Every skew - symmetric matrix of odd order is invertible.
(C) If A is a non-singular matrix, then A^-1 is skew-symmetric.
(D) The adjoint of a diagonal matrix is a diagonal matrix.
Choose the correct answer from the options given below :

A. If A and B are two invertible matrices, then (AB)^-1 = A^-1 B^-1
B. Every skew-symmetric matrix of odd order is invertible
C. If A is non-singular matrix, then (A^T)^-1 = (A^-1)^T
D. If A is an involutory matrix, then (I+A) (I-A) = 0
E. A diagonal matrix is both an upper triangular and a lower triangular
Choose the correct answer from the options given below :

If x,y,z are all distinct and =0, then the value of xyz is

If A = and B = , what is the value of (2A-3B)?

If A= B= and C = . The value of A+ (B+C) is

For Matrix , the sum and differences of maximum & minimum 1 eight value of Matrix are 4 and 8, then the eigen values for the Matrix A are.

The system matrix of a linear time invariant continuous time system is given by
What are the roots of characteristics equation.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The state transition matrix represents the free response of the system.
Reason R: The state transition matrix satisfies the homogeneous state equation
In the light of the above statements, choose the most appropriate answer from the options given below :

The bus admittance matrix of a power system is given as.
1 2 3

The impedance of line between bus 2 and bus 3 will be equal to____

A solar photovoltaic system feeds power to a motor of 1hp at the shaft. The motor has an efficiency of 85%. Each module has 40 multi crestline Silicone solar cells arranged in 9x5 matrix? The cell is 130 mm×130 mm and the cell efficiency is 13%. Calculate the number of photovoltaic modules required, assuming global radiation incident to the panel as 1kW/m²

If and I = unit matrix, then the value of is:

Any square matrix A can be expressed as:
1. The product of a symmetric and a skew-symmetric matrices.
2. The division of a symmetric matrix by a skew-symmetric matrix.
3. The sum of a symmetric and a skew-symmetric matrices.
4. The subtraction of a symmetric from a skew-symmetric matrix.

If X is a square matrix of order NxN, then for any constant c, |cX| is equal to,

If X and Y are invertible matrices of same order then