# Column Space of a matrix -Row operations [closed]

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?

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

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• Think about elementary row operations in terms of matrix operators. Are these elementary matrices of full rank? – jaslibra Apr 7 '18 at 12:30
• @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/… – gimusi Apr 10 '18 at 12:19

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