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Math Help - Find a basis for...

  1. #1
    Junior Member piglet's Avatar
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    Find a basis for...

    In R4,

    U = <(1,1,0,0) , (0,1,0,2)>.

    I want to find a basis for the orthogonal complement U(perp) of U


    I know U(perp) can be found by getting the null-space of U

    i.e. solving Ux = 0 where x = column vector x1, x2, x3, x4

    however im becoming unstuck,

    solving Ux = 0 leaves me with (1) x1 + x2 = 0
    (2) x2 + 2x4 = 0

    2 equations with 3 unknowns means i can solve for 2 variables...?


    What variables should i pick as being "free" variables?
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  2. #2
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    Quote Originally Posted by piglet View Post
    In R4,

    U = <(1,1,0,0) , (0,1,0,2)>.

    I want to find a basis for the orthogonal complement U(perp) of U

    I know U(perp) can be found by getting the null-space of U

    i.e. solving Ux = 0 where x = column vector x1, x2, x3, x4

    however im becoming unstuck,

    solving Ux = 0 leaves me with (1) x1 + x2 = 0
    (2) x2 + 2x4 = 0

    2 equations with 3 unknowns means i can solve for 2 variables...?


    What variables should i pick as being "free" variables?

    Strange question... x_3 can be anything, and if you fix x_2\,,\,\,then\,\,\,x_1=-x_2\,,\,\,x_4=-\frac{1}{2}x_2 , so ...

    Tonio
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  3. #3
    Junior Member piglet's Avatar
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    Quote Originally Posted by tonio View Post
    Strange question... x_3 can be anything, and if you fix x_2\,,\,\,then\,\,\,x_1=-x_2\,,\,\,x_4=-\frac{1}{2}x_2 , so ...

    Tonio

    thanks alot, I reckon i can finish the problem from there.
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