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 ⎡⎣⎢⎢

Question

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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Margaret 1 week 2021-11-22T06:41:49+00:00 1 Answer 0 views 0

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    2021-11-22T06:43:44+00:00

    Answer:

    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, <a,b,c> 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:

    <a,b,c> = <6,-5,-5>×<7,4,6>= <-10,-71,59>

    so, the homogeneous system is:

    -10x-71y+59z=0

    by replacing the vector <3,x,y> 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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45:7+7-4:2-5:5*4+35:2 =? ( )