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Thread: Find a set of vectors whose span is the kernel of the following matrix.

  1. #1
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    Find a set of vectors whose span is the kernel of the following matrix.

    Find a set of vectors whose span is the kernel of the following matrix:

    1 1 2 0
    2 1 0 -1
    0 1 4 1

    When I calculate the kernel I get:

    2s+t
    -4s-t
    s
    t

    To find the set of vectors that span this kernel do I factor out the s and t?

    s * [2, -4, 1, 0]T + t * [1, -1, 0, 1]T

    Am I close on this one?
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  2. #2
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    Re: Find a set of vectors whose span is the kernel of the following matrix.

    correct

    The two vectors $\displaystyle \{\{1,-1,0,1\},\{2,-4,1,0\}\}$ form a basis for the kernel of the matrix
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  3. #3
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    Re: Find a set of vectors whose span is the kernel of the following matrix.

    So I am assuming that I would leave out the constant multipliers s and t?
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  4. #4
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    Re: Find a set of vectors whose span is the kernel of the following matrix.

    Saying that "{{1, -1, 0, 1}, {2, -4, 1 , 0}} is a basis for the kernel" means that any vector in the kernel can be written in the form s{1, -1, 0, 1}+ t{2, -4, 1, 0} for numbers s and t. Those are just two different ways of saying the same thing.
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