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The particular integral of (4D^{2} + 4D + 1) y = 8e^{x/2} is
The vector [1, 2, 3], [1, 0, 0], [0, 1, 0], [0, 0, 1] are
Let a = [1, 2, 3], b = [1, 0, 0], c = [0, 1, 0]
d = [0, 0, 1]
a = b + 2c + 3d
Therefore, vector a, b, c, d are linearly dependent.
Projection of vactor
Kroncker delta S^{i}_{j} is a mixed tensor of rank _____
Real part of the is ______ (upto two decimal places)
Given z^{3} = 1. Let z_{0},z_{1} and z_{2} be the complex roots of the above equation.If z_{0} = 1, then the value of z_{1}z_{2} is ____ (Answer should be an integer)
Find the value of integral, is ____ (upto one decimal place)
The dimensionality of the vector space of hermitian 3 x 3 matrices is ____ (answer should be an integer)
For the Hermitian
Therefore, a_{ii} are real but a_{ij} (j≠i) can be complex.
For n x n Hermitiain matrices,
Therefore, for 3 x 3 Hermitian matrices, number of independent entries in the matrices = 3^{2} = 9 Dimentionality = 9
Given vector the line integral where C is a circle of radius 5 units with its center at origin is ________
The determinant of the metric tensor corresponding to ds^{2} = 5(dx^{1})^{2} + 3(dx^{2})^{2} + 4(dx^{3})^{2}  6dx^{1}dx^{2 }+ 4dx^{2}dx^{3} is
Comparing with equation standard expression for the metric tensor
Consider a vector v = (v_{1}, v_{2}, v_{3}) in three dimensional complex vector space c^{3}. A linear operator T is designed as follows
T( v_{1}, v_{2,} v_{3}) = ( v_{1,} v_{2}  v_{3,}iv_{2})
Find T^{+ }matrix representation using orthonormal basis
Given the Legendre polynomial P_{0}(x) = 1, P_{1 }(x) = x and then polynomial (3x^{2} + x 1)
Polynomial, 3x^{2} + x  1
A square matrix A is said to be orthogonal if AA^{T} = A^{T}A = 1
for orthogonal a^{2} + b^{2} = 1
Therefore,
Find the complex coefficient Cn of the fourier series of the function for n is odd.
C_{n} = 1/ inπ
The equation of the plane that is tangent to the surface xyz = 8 at point (1,2,4) is
Suppose T(x,y,z) be any point on tangent plane is normal to surface at point P(1,2,4). Therefore, is perpendicular to vector lying in the tangent plane of the given surface.
The value of the integral is ______ (upto two decimal places)
The value of the Contour integral
and the contour C is a circle of radius 2 centred at the origin traversed in the counterclockwise direction is ______ (answer should be an integer).
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