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Math Help - Linear algebra: Basis, Nullspace, Subspace

  1. #1
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    Linear algebra: Basis, Nullspace, Subspace

    Your Help is greatly appreciated. Thanks in advance. I am having a hardtime with these three problems.

    1) Find the basis for Nullspace of A if A equals

    1 2 -3
    2 1 0
    -2 -1 3

    2) Let W be the subspace of R^(4) spanned by vectors (1,-2,5,3)^(T),
    (2,3,1,-4)^(T), (3,8,-3,-5)^(T). Extend the basis of W to a basis of the whole space of R^(4).
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by googoogaga View Post
    Your Help is greatly appreciated. Thanks in advance. I am having a hardtime with these three problems.

    1) Find the basis for Nullspace of A if A equals

    1 2 -3
    2 1 0
    -2 -1 3

    you have 2 problems here

    The null space of a matrix A, is the set of all matrices \bold{x} such that A \bold{x} = \bold{0}

    thus you need to find the solution set to: \left( \begin{array}{ccc} 1 & 2 & -3 \\ 2 & 1 & 0 \\ -2 & -1 & 3  \end{array} \right) \left( \begin{array}{c} x_1 \\ x_2 \\ x_3  \end{array} \right)  = \left( \begin{array}{c} 0 \\ 0 \\ 0  \end{array} \right)
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  3. #3
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    I now understand that Nullspace of A is (0, 0, 0)^(T), but what is the basis for the nullsapce. Was is a simple definition for basis, and how do you find it?
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