Math Help Forum - View Single Post - linear algebra- vector-basis-subspace

arbolis · #7 October 10th, 2008, 09:23 PM

Quote:

Originally Posted by watchmath

Yes in this case you can choose that one.

Now suppose we have a matrix A where the vector columns of A are $c_1,c_2,c_3,c_4$ and suppose by row operation we can reduce A into
$\begin{pmatrix}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&0\end{pmatrix}$ .

What are the generators of the subspace generated by $c_1,c_2,c_3,c_4$ ?

I'd say $c_1$ , $c_2$ and $c_3$ . I can add that I'd say it to be true even if we had the matrix $\begin{pmatrix}1&0&0&89\\0&1&0&0\\0&0&1&0\\0&0&0&0\end{pmatrix}$ . I hope I'm right.