Find a set of vectors in [itex]\mathbb{R}^3[/itex] that spans the subspace(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

S\,=\,\{\,u\,\in\,\mathbb{R}^3\,|\,u\cdot v\,=\,0\,\}

[/tex]

where v=<1,2,3>

Maybe 12 hours of studying is too much and I'm fried or, maybe I'm looking for excuses. Either way...

To solve this I'm trying to set up a matrix multiplication and augment it at zero. But, I just get a single linear equation which tells me that the only way I can have a span of this subspace is if my other vector is the zero vector <0,0,0>. I don't think that's right.

[tex]

\begin{bmatrix}

a & b & c

\end{bmatrix}

*

\begin{bmatrix}

1\\2\\3

\end{bmatrix}

=

\mathbf{0}

[/tex]

Getting [itex]a+2b+3c=0[/itex]

Where's my issue?

Thanks.

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# Homework Help: Find a set of vectors that spans the subspace

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