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

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?

• A plane. One axis vertical and another between the x and y axes. – Tucker Jun 3 '17 at 5:18
• 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. – Paul Sundheim Jun 3 '17 at 5:19
• which plane please give some more explanation – 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 $\mathbb{R}$.
• yes but i am able to visualize which plane in $\mathbb{R}^3$ it spans – dipali mali Jun 3 '17 at 6:20