• Cyberian's Gold

    @zaasmi said in MTH603 Grand Quiz Solution and Discussion:

    The Jacobi iteration converges, if A is strictly diagonally dominant.

    If A is strictly row diagonally dominant, then the Jacobi iteration converges for any choice of the initial approximation x(0). However, the Jacobi iteration may converge for a matrix that is not strictly row diagonally dominant.

  • Cyberian's Gold

    The Jacobi iteration converges, if A is strictly diagonally dominant.

  • Cyberian's Gold

    The linear equation 2x+0y-2=0 has----- solution(s).

    Answer

  • Cyberian's Gold

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  • Cyberian's Gold

    Let[A]bea3×3realsymmetricmatrixwith|a23|bethenumericallylargestoff−diagonalelementthenusingJacobi′smethodthevalueofθcanbefoundby

    Let A be a 3×3 matrix with real entries. Prove that if A is not similar over
    R to a triangular matrix then A is similar over C to a diagonal matrix.

  • Cyberian's Gold

    While using Relaxation method, which of the following is increment ‘dxi’corresponding to the largest Residual for 1st iteration on the system;
    2x+3y = 1, 3x +2y = - 4 ?

  • Cyberian's Gold

    Central Difference method is the finite difference method

    Finite difference. A finite difference is a mathematical expression of the form f (x + b) − f (x + a). … The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems.

  • Cyberian's Gold

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  • Cyberian's Gold

    Whileusingtherelaxationmethodforfindingthesolutionofthefollowingsystem11x1+x2−x3=8 x1+8x2+5x3=9 x1+x2+9x3=7withtheinitialvector(0,0,0),theresidualswouldbe

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  • Cyberian's Gold

    By using determinants, we can easily check that the solution of the given system of linear equation ______ and it is ______.

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  • Cyberian's Gold

    If the determinant of a matrix A is not equal to zero then the system of equations will have……….

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    A nxn nonhomogeneous system of linear equations has a unique non-trivial solution if and only if its determinant is non-zero. If this determinant is zero, then the system has either no nontrivial solutions or an infinite number of solutions.

  • Cyberian's Gold

    For the system of equations; x =2, y=3. The inverse of the matrix associated with its coefficients is-----------.

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  • Cyberian's Gold

    While using Jacobi method for the matrix
    A=⎡⎣⎢⎢11/41/21/41/31/41/21/41/5⎤⎦⎥⎥

    the value of ‘theta θ’ can be found as

    fe720b54-d7e6-4e4a-babe-a5adb19733b4-image.png

  • Cyberian's Gold

    If the Relaxation method is applied on the system; 2x+3y = 1, 3x +2y = - 4, then largest residual in 1st iteration will reduce to ---------.

    7f0b082c-7e56-45fa-ac8f-1e6e548b558e-image.png

  • Cyberian's Gold

    Whichofthefollowingisaforwarddifferencetableforthegivenvaluesofxandy?xy0.10.0030.50.1480.90.37

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  • Cyberian's Gold

    While using Relaxation method, which of the following is the largest Residual for 1st iteration on the system;
    2x+3y = 1, 3x +2y = - 4 ?

    6ada249a-e9e3-41f8-aff2-6f78a63cb939-image.png

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