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Math Help - NullSpace

  1. #1
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    NullSpace

    Let S be the subspace of R4 given by the solution set of the equations
    -x3 + 4 x4 = -x2 - x3 + x4 and -x1 - x3 = -x1 - 3 x3 = x2

    An example of a matrix for which S is the nullspace is....

    i tried doing 1 1 0 0
    0 1 0 3
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  2. #2
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    Quote Originally Posted by ah-bee View Post
    Let S be the subspace of R4 given by the solution set of the equations
    -x3 + 4 x4 = -x2 - x3 + x4 and -x1 - x3 = -x1 - 3 x3 = x2

    An example of a matrix for which S is the nullspace is....

    i tried doing 1 1 0 0
    0 1 0 3
    -x_3 + 4 x_4 = -x_2 - x_3 + x_4 \Rightarrow x_2 = -3 x_4 .... (1)

    -x_1 - x_3 = -x_1 - 3 x_3 \Rightarrow x_3 = 0 .... (2)

    -x_1 - x_3 =  x_2 \Rightarrow x_1 = -x_3 - x_2 .... (3)
    Substitute from (1) and (2): x_1 = 3 x_4.

    So elements of S have the form x_4 (3, -3, 0, 1).

    So the example you propose works.
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  3. #3
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    the problem is.. when i enter my solution into the web page (online assignment), it says that it is wrong. any ideas why?
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  4. #4
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    Quote Originally Posted by ah-bee View Post
    the problem is.. when i enter my solution into the web page (online assignment), it says that it is wrong. any ideas why?
    1. Perhaps a 4x4 matrix is wanted ....? In which case the question should be more specific on the dimension required.

    2. Have you correctly copied the system of equations?
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  5. #5
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    1. I gave a 2x4 matrix in a similar practice question and got it right + there are no specific matrix dimensions required.

    2. Yeah, I've copied the equations down correctly.
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