How do you go about finding certain vectors from Span(D) to represent axes and planes?? I'm not entirely sure how to go about doing these questions!
2026-04-05 21:28:39.1775424519
Finding Span(D) from a vector of R^3
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You can think of the Span of a set of vectors as the places you can reach via linear combinations of the specified vectors. Essentially, where you can get to by multiplying vectors by constants and adding them together. For instance, if you have unit vectors $<1,0>$ and $<0,1>$ you can "span" the entire plane $\mathbb{R}^2$ since you can reach any point in $\mathbb{R}^2$ with some combination $a<1,0> + b<0,1>$ for some $a,b \in \mathbb{R}$. For example, if you wanted to get to the point $(4,5)$ you could simply have $4<1,0> + 5<0,1>$. From this example you may be able to see that these vectors can clearly "span" all of $\mathbb{R}^2$ as they can reach any point in that space.