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A matrix A such that A^{m} = 0 for some positive integer and A^{k} ≠ 0 for any k < m, is said to be
Transpose of a matrix happens to be equal to the negative of itself, then one can say that the matrix is skew symmetric.
In mathematics, particularly in linear algebra, a skewsymmetric 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 matrix A = [a_{ij}] ∈ M_{n} is said to be Hermitian if A = A^{* } or
= a_{ij}, for a_{ji} only.
A matrix A = [a_{ij}] ∈ M_{n} is skewHermitian if A = − A ^{*}
If A and B are two odd order Skew — symmetric matrices such that AB = BA, then what is the matrix AB?
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
(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?
If A = satisfies the matrix equation A^{2} — kA + 2I = 0, then what is the value of k?
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
(y^{2} – 3xy)dx + (x^{2 }– xy)dy = 0 is
(y^{2} – 3xy)dx + (x^{2} – xy) dy = 0;
M = y^{2} – 3xy, N = x^{2} – xy
Here differential equation is homogeneous, then
Mx + Ny = xy^{2} – 3x^{2}y + x^{2}y – xy^{2} = – 2x^{2}y ≠ 0
the product of two unitary matrices is always unitary.
The points ( x_{1, }y_{1} ) , ( x_{2}, y_{2}), ( x_{3,} y_{3}) are collinear if the rank of the matrix is
A neccessary condition for the linear equations a_{1}x + b_{1} = 0 and a_{2}x + b_{2} = 0, to have a common solution is that
A necesary and sufficient condition for the linear equations a_{1}x + b_{1}y + c_{1} = 0 and a_{2}x + b_{2}y + c_{2} = 0 to possess a unique solution is that
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?
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