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13 February, 23:58

The following two vectors satisfy the same system of linear equations. u=⎡⎣⎢⎢6-5-5⎤⎦⎥⎥, v=⎡⎣⎢⎢746⎤⎦⎥⎥ Find x and y that make the vector ⎡⎣⎢⎢3xy⎤⎦⎥⎥ a solution to the corresponding homogeneous system:

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  1. 14 February, 00:10
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    x=-30/71, y=0

    Step-by-step explanation:

    if a vector satisfies an equation of the form ax+by+cz=0 then the vector is

    parallel to the plane ax+by+cz=0, and, the cross product of two vectors results in an orthogonal vector to both.

    So, the normal vector of the plane ax+by+cz=0, can be found as the cross product of the two parallel vetors to the plane:

    = * =

    so, the homogeneous system is:

    -10x-71y+59z=0

    by replacing the vector in the system

    -30-71x+59y=0

    So, there are 2 unknown variables and 1 equation, it means that 1 variable is free

    so, y=0 is a random defition and x can be obtain with the equation

    -30-71x=0 - > x=-30/71
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