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The particular integral of (4D2 + 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.
The projection of vector on vector
Projection of vactor
Find an of a Fourier series for |x|, -π < x < π
Real part of the is ______ (upto two decimal places)
Given z3 = 1. Let z0,z1 and z2 be the complex roots of the above equation.If z0 = 1, then the value of z1z2 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, aii are real but aij (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 = 32 = 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 ds2 = 5(dx1)2 + 3(dx2)2 + 4(dx3)2 - 6dx1dx2 + 4dx2dx3 is
Comparing with equation standard expression for the metric tensor
Consider a vector v = (v1, v2, v3) in three dimensional complex vector space c3. A linear operator T is designed as follows
T( v1, v2, v3) = ( v1, v2 - v3,iv2)
Find T+ matrix representation using orthonormal basis
Given the Legendre polynomial P0(x) = 1, P1 (x) = x and then polynomial (3x2 + x -1)
Polynomial, 3x2 + x - 1
The matrix A defined by is orthogonal if
A square matrix A is said to be orthogonal if AAT = ATA = 1
for orthogonal a2 + b2 = 1
Find the inverse Laplace transform of f(s) =
Find the complex coefficient Cn of the fourier series of the function for n is odd.
Cn = 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).