A matrix A such that A2 = A, is called
Consider the matrix A = Then,
A matrix A such that A2 = I, is called
A matrix A such that Am = 0 for some positive integer and Ak ≠ 0 for any k < m, is said to be
A square matrix A such the AT = —A, is called a
Transpose of a matrix happens to be equal to the negative of itself, then one can say that the matrix is skew symmetric.
A square matrix A such that AT = -A, is called a
In mathematics, particularly in linear algebra, a skew-symmetric matrix is a square matrix whose transpose equals its negative.
Mark the in correct statement. If A* and B* are the transpose of the conjugates of A and B respectively, the n
A square matrix A is said to be Hermitian Matrix if
A matrix A = [aij] ∈ Mn is said to be Hermitian if A = A* or
= aij, for aji only.
A square matrix A is said to be Skew Hermitian Matrix, if
A matrix A = [aij] ∈ Mn is skew-Hermitian if A = − A *
If A and B are two odd order Skew — symmetric matrices such that AB = BA, then what is the matrix AB?
Mark the incorrect statement
The diagonal elements of a Skew Hermitian Matrix are
To convert a Hermitian Matrix into Skew Hermitian Matrix, the Hermitian Matrix must be multiplied by
Which is not correct? If A is any square matrix, then... is Hermitian Matrix
Every square matrix is uniquely expressible as
If A is any square matrix, then A — A' is a
(A − A')' = A' − (A')'
= A' − A
= −(A − A')
Therefore, it is a skew symmetric matrix
If A and B are symmetric matrices of the same order, then which one of the following is not correct?
A square matrix A is said to be ... if AAT = I
If A = satisfies the matrix equation A2 — kA + 21 = 0, then what is the value of k?
A square matirx A is said to be .... if A* A = I
Under which one of the following condition does the system of equations have a unique solution?
One of the integrating factor of the differential equation
(y2 – 3xy)dx + (x2 – xy)dy = 0 is
(y2 – 3xy)dx + (x2 – xy) dy = 0;
M = y2 – 3xy, N = x2 – xy
Here differential equation is homogeneous, then
Mx + Ny = xy2 – 3x2y + x2y – xy2 = – 2x2y ≠ 0
The product of two orthogonal matrices is a ... matrix
The product of two Unitary matrices is a ________ matrix
the product of two unitary matrices is always unitary.
The points ( x1, y1 ) , ( x2, y2), ( x3, y3) are collinear if the rank of the matrix is
A neccessary condition for the linear equations a1x + b1 = 0 and a2x + b2 = 0, to have a common solution is that
A necesary and sufficient condition for the linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 to possess a unique solution is that
The value of the determinant is
Which of the following statement is incorrect?
Let A and B be any two n x n matrices and tr(A) = Consider the following statement
I. tr(AB) = tr(BA)
II. tr(A + B) = tr. (A) + tr(B)
Which of the following statement given above is/are correct?