Jacobian matrix For f(x, y) = e" cos(y) + xe³9 – 2, calculate the Jacobian row vector J.
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A: This can be found by using the formula 1(x2+y2+z2)200400300400003000-100122 = xyz
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Q: 6ij=I , V i,j from 1 to 3 where I is identity tensor matrix. 0 صواب ihi O
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- Find the flux of the vector v=⟨x,y,z⟩ along the surface of the right tetrahedron below. Please show full solution legibly. Thanks!Find the centroid (¯x,¯y) of the triangle with vertices at (0,0)(1,0) and (0,5) x¯= y¯=apply Jacobi's method to the given system.Take the zero vector as the initial approximation and work with four-significant- digit accuracy until two successive iterates agree within 0. 001 in each variable. In each case, compare your answer with the exact solution found using any direct method you like. 3a + b = 1 a+ 4b+ c = 1 b + 3c = 1
- IntegrateF(x, y, z) = z, over the portion of the plane x + y + z = 4 that lies above the square 0<= x <= 1, 0<=y<=1, in the xy-planein b part, system gives an error that t is not defined for the frictionless spring question.Consider a point particle with position vector r = (x, y, z) in Cartesian coordinates, moving with a velocity v = (β, αz, −αy), where α and β are positive constants. Find the general form of r(t), the position of the particle, as a function of time t, (hint: write v = (β, αz, −αy) as a system of first order ODEs and note that the equation for x is decoupled from the others). Describe in words the motion of the particle and sketch its trajectory in R3 (you can use software packages for the plot).