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?

  • $\begingroup$ 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

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

  • $\begingroup$ 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

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