-2
$\begingroup$

I know that Row operations do not change the Row space of a matrix but how to know whether they have any effect on the column space or not? I tried to search but could not find a suitable explanation for this question. Please give some explanation, do elementary Row operations change the Column Space of a matrix?

$\endgroup$

closed as off-topic by GNUSupporter 8964民主女神 地下教會, Saad, Shaun, jvdhooft, Arturo Magidin Apr 7 '18 at 12:55

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – GNUSupporter 8964民主女神 地下教會, Saad, Shaun, jvdhooft, Arturo Magidin
If this question can be reworded to fit the rules in the help center, please edit the question.

  • 1
    $\begingroup$ Welcome to Math.SE! Please read this post and the others there for information on writing a good question for this site. In particular, people will be more willing to help if you edit your question to include some motivation, and an explanation of your own attempts. $\endgroup$ – GNUSupporter 8964民主女神 地下教會 Apr 7 '18 at 12:28
  • $\begingroup$ Think about elementary row operations in terms of matrix operators. Are these elementary matrices of full rank? $\endgroup$ – jaslibra Apr 7 '18 at 12:30
  • $\begingroup$ @KalitGautam Please remember that you can choose an answer among the given if the OP is solved, more details here meta.stackexchange.com/questions/5234/… $\endgroup$ – gimusi Apr 10 '18 at 12:19
1
$\begingroup$

Yes of course, row operations preserves row space but in general not the colums space.

Let consider for example

$$\left(\begin{array}{rrr} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right)\stackrel{R3-R2}\to\left(\begin{array}{rrr} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 0 & 0 & 0\end{array}\right)$$

$\endgroup$

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