0
$\begingroup$

This is what I'm having a little bit of trouble with this question: given four

\begin{bmatrix}{3}\\{2}\\{-4}\end{bmatrix}\begin{bmatrix}{-6}\\{1}\\{7}\end{bmatrix}\begin{bmatrix}{0}\\{-5}\\{2}\end{bmatrix}\begin{bmatrix}{3}\\{7}\\{-5}\end{bmatrix}

Now the question asks for a basis of the subspace spanned by the {u,v,w,z}, which are the respective vectors I posted above.

The book places the above vectors into ROWS, not columns and I am a bit perplexed why. The correct answer here is just the first 3 vectors, but IM curious why the entires are placed in columns, not rows. The row reduction math is easy.

This is the form they started the row operations:

\begin{bmatrix}{3}&{2}&{-4}\\{-6}&{1}&{7}\\{0}&{-5}&{2}\\{3}&{7}&{-5}\end{bmatrix}

$\endgroup$
  • $\begingroup$ Better to put them in columns and perform RREF. Three is a party, four is a crowd. One needs to go. I also don't know why they are put in columns. And I can see that the vectors aren't happy about it...:) $\endgroup$ – imranfat Apr 23 '16 at 0:37
  • $\begingroup$ Well you cant just eliminate one, so that's why they entered them this way . But is there any particular logic behind it? $\endgroup$ – Charles Johnson Apr 23 '16 at 0:51
  • $\begingroup$ I don't see the logic to put them in that notation. Like you said, put them behind each other and perform RREF. $\endgroup$ – imranfat Apr 23 '16 at 0:53
0
$\begingroup$

Elementary row operations (EROs) preserve the row space of a matrix. So sticking the vectors in the rows of a matrix and performing EROs will be a very convenient way to get a basis for the space. Not only will you get a basis, but you'll often get a nicer basis (more zeros) than just figuring out a maximal linearly independent subset of your original vectors.

$\endgroup$
  • $\begingroup$ Some textbooks consistently put vectors in rows, others use columns. Strictly speaking for its purpose, it doesn't really matter for the question. The same I see when dealing with Markov and Leontief matrices. Column notation works nice for the TI, so I always put vectors in columns. . $\endgroup$ – imranfat Apr 23 '16 at 1:11

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.