• Cyberian's Gold

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

    907bdf8f-c194-4fcb-ba4b-0e455ae430ec-image.png

    9c780b0d-13d6-4eb3-ab0f-8abfeb9d2856-image.png

  • Cyberian's Gold

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

    ae4fbbdd-0cf8-4d8c-9ce9-0c806d030d5d-image.png

  • Cyberian's Gold

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

    3a0c43d7-6890-4d0d-9034-5859c7f4def7-image.png

    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-----------.

    1489d9aa-bc16-4375-a675-9915e41cde4f-image.png

  • 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

    1747720b-4bf6-4799-aaa7-6af85beb7d1c-image.png

    134ea9b4-b980-4597-b3e5-2334b6eb7718-image.png

  • 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

  • Cyberian's Gold

    Let [A] be a 3x3 real symmetric matrix with
    |a12|
    be numerically the largest off-diagonal element of A, then we can construct orthogonal matrix S1 by Jacobi’s method as

    4980db70-06a2-475b-85be-2db41ae321aa-image.png

  • Cyberian's Gold

    The number of significant digits in the number 608.030060 is:

    9

  • Cyberian's Gold

    For two matrices A and B, such that “A = Inverse of B”, then which of the following is true?

    00a82a83-0a86-4876-9075-20994b70d8f9-image.png

  • Cyberian's Gold

    The 2nd row of the augmented matrix of the system of linear equations is:
    2x+z=4
    x-y+z=-3
    -y+z=-5

  • Cyberian's Gold

    If a system of equations has a property that each of the equation possesses one large coefficient and the larger coefficients in the equations correspond to different unknowns in different equations, then which of the following iterative method id preferred to apply?

    40e4730b-158a-4d6b-82a7-12e087f638cc-image.png

  • Cyberian's Gold

    While solving by Gauss-Seidel method, which of the following is the first Iterative solution for the system; x-2y =1, x+4y=4 ?

    a) (1, 0.75)
    b) (0.25,1)
    c) (0,0)
    d) (1,0.65)

    42ed2433-93ba-448b-a824-e81e1330f787-image.png

  • Cyberian's Gold

    The dominant eigenvector of a matrix is an eigenvector corresponding to the eigenvalue of largest magnitude (for real numbers, smallest absolute value) of that matrix.

    Eigenvectors of a matrix corresponding to distinct eigenvalues are linearly independent. ▫. If λ is an eigenvalue of multiplicity k of an n × n matrix A, then the number of … power method converges to the smallest eigenvalue in absolute value of A. … v2, …, vn, and that λ1 is a simple eigenvalue with the largest magnitude, i.e.,.

  • Cyberian's Gold

    While using the Gauss-Seidel Method for finding the solution of the system of equation, the following system
    2x+y−3z=5
    x+3y+2z=7
    x+2y+z=3

    can be rewritten as

    a20e9c25-3389-4217-8e90-27f890f28ae3-image.png

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