what is span of (1,1,1) and (0,1,1) in $\mathbb{R}^3$?

I know that these two vectors are linearly independent in $\mathbb{R}^3$ but what is span?

  • $\begingroup$ A plane. One axis vertical and another between the x and y axes. $\endgroup$ – Tucker Jun 3 '17 at 5:18
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    $\begingroup$ The span is the collection of elements of the form $a(1,1,1) + b(0,1,1)$ where $a$ ande $b$ are real numbers. $\endgroup$ – Paul Sundheim Jun 3 '17 at 5:19
  • $\begingroup$ which plane please give some more explanation $\endgroup$ – dipali mali Jun 3 '17 at 8:44

The span consists of all linear combinations of (1,1,1) and (0,1,1), that is, the set of elements ($x$,$x+y$,$x+y$) for all $x,y \in \mathbb{R}$. Notice that this is isomorphic to $\mathbb{R}^2$ over $\mathbb{R}$.

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  • $\begingroup$ yes but i am able to visualize which plane in $\mathbb{R}^3$ it spans $\endgroup$ – dipali mali Jun 3 '17 at 6:20

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