Question

do the points P(2,1,4), Q(0,1,5) and R(-4,1,7) lie on the same line as R^3?

Answer 1

Does this have something to do with linear independence?

Answer 2

if you use elimination, I think you get 2 pivots. This suggests a plane to me.

Answer 3

Yeah I got two pivots forming a matrix, so how do you know when it's on a line?

Answer 4

Only 1 pivot.

Answer 5

Ohhhh that would make a lot of sense, so any thing more than one is a plane?

Answer 6

n pivots means
\[R^{n}\]
so n=1 is a line, n=2 is a plane, n=3 is 3 dimensional space, and so on..

Answer 7

kk thanks a lot