0
$\begingroup$

So i have this question :

The number of columns of a matrix gives the dimension of the span of the column vectors.

I know that the answer is indeed FALSE.

But i want to back my answer up with a simple, right, yet CONCRETE explanation of why that is so.

I was thinking : the question if false due to the fact that the dimension o of the span of the column vectors is given by the maximum amount of linearly independent vectors.

is that correct?

$\endgroup$
  • $\begingroup$ Yeah, for instance you can just make all the columns scalar multiples of the first. Or, even worse, consider the zero matrix. $\endgroup$ – Kaj Hansen Jun 19 '18 at 8:37
1
$\begingroup$

Take then null $n\times n$ matrix. It has $n$ columns, but the dimension of the span of the column vectors is $0$.

$\endgroup$
  • $\begingroup$ Hi carlos. I see you've really helped me a lot these past few days, and as, due to my insecurities ,i have asked a lot of questions on this website, i got question blocked. So i was willing to ask you , as i have , tommorrow, my most important exam , which is indeed maths, if you could genuinely help me with my last question , if i post it here as an image ? it would be so useful , seriously . thanks if you do $\endgroup$ – Michael Morello Jun 19 '18 at 17:09
  • $\begingroup$ @MichaelMorello Do a Google search for my name. You'll find my web page, at the bottom of which there's my e-mail address. $\endgroup$ – José Carlos Santos Jun 19 '18 at 17:12
  • $\begingroup$ I sent you an email $\endgroup$ – Michael Morello Jun 19 '18 at 17:23
  • $\begingroup$ May i ask you if you receieved it? $\endgroup$ – Michael Morello Jun 19 '18 at 17:51

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.