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Math Help - What is the dimension of V ? Find a basis for V

  1. #1
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    What is the dimension of V ? Find a basis for V

    Just question (c). And only the first couple of steps.

    Any help is appreciated!
    Attached Thumbnails Attached Thumbnails What is the dimension of V ? Find a basis for V-q10.jpg  
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  2. #2
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    \begin{bmatrix}<br />
1 & 0\\ <br />
2 & 1\\ <br />
0 & 2\\ <br />
3 & 1<br />
\end{bmatrix}<br />
rref= \begin{bmatrix}<br />
1 & 0\\ <br />
0 & 1\\ <br />
0 & 0\\ <br />
0 & 0<br />
\end{bmatrix}

    The row rank is 2.

    x_1=0 and x_2=0.

    The nullity is \mathbf{0}.
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  3. #3
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    Quote Originally Posted by dwsmith View Post
    \begin{bmatrix}<br />
1 & 0\\ <br />
2 & 1\\ <br />
0 & 2\\ <br />
3 & 1<br />
\end{bmatrix}<br />
rref= \begin{bmatrix}<br />
1 & 0\\ <br />
0 & 1\\ <br />
0 & 0\\ <br />
0 & 0<br />
\end{bmatrix}

    The row rank is 2.

    x_1=0 and x_2=0.

    The nullity is \mathbf{0}.

    What is the basis?
    Last edited by DarK; October 24th 2010 at 08:38 AM.
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  4. #4
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    Nullity = Dim

    The basis are the vectors that span the nullity.
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