describe geometrically span({(1,-2, 1),(-2,4, -2)})? a line, a plane, a hyperplane?

how do I do this?

Question

describe geometrically span({(1,-2, 1),(-2,4, -2)})? a line, a plane, a hyperplane?

how do I do this?

ybarrap · Answer

@Loser66

loser66 · Answer

I am not sure about this. if (1,-2,1) and (-2,4,-2) are points, then, they span a line
if they are vectors, then they span a plane

ybarrap · Answer

Note that the second vector is a function of the 1st.

anonymous · Answer

they are vectors

loser66 · Answer

oh yea!! they are linearly dependent vectors---> span a line only, hehehe

anonymous · Answer

ok. so if they are linearly dependent vectors then they span a line. then if they are linearly independent then they span a plane?

loser66 · Answer

yup

anonymous · Answer

ok great. thanks! last thing what does it mean if they are all of 3 space?

loser66 · Answer

don't understand the question. Do you mean 3D?

anonymous · Answer

haha no problem. its just what my prof uses. I dont really know Ill check the book