3x+2y+7z=0,4x-3y-2z=0,5x+9y+23z=0 solve the following system of homogeneous equations

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3x+2y+7z=0,4x-3y-2z=0,5x+9y+23z=0 solve the following system of homogeneous equations

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Ariana 3 days 2021-10-11T05:33:23+00:00 1 Answer 0 views 0

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    2021-10-11T05:35:02+00:00

    Given:

    3x + 2y + 7z = 0, 4x – 3y – 2z = 0, 5x + 9y + 23z = 0

    To find:

    Solve the following system of homogeneous equations

    Solution:

    From given, we have the system of homogeneous equations

    3x + 2y + 7z = 0……(1)

    4x – 3y – 2z = 0……..(2)

    5x + 9y + 23z = 0 …….(3)

    (1) × 4 – (2) × 3 gives,

    12x + 8y + 28z = 0

    12x – 9y – 6z = 0

    solving these equations, we get,

    17y + 34z = 0

    y = – 2z

    equating the value of y in equation (1), we get,

    3x + 2(-2z) + 7z = 0

    3x – 4z + 7z = 0

    3x + 3z = 0

    x = -z

    Therfore, the solutions of the given system of equations, we have,

    x = -z and y = -2z

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