Thread: explicit description of a line?

Find an explicit description of the line 3x+2y = 0 in R2 through the origin.

the answer is:
span {[2, -3]} , but how?

The line in is spanned by any nonzero vector such that lies on the line. is one such vector; another would be .

Originally Posted by yangx

Find an explicit description of the line 3x+2y = 0 in R2 through the origin.
the answer is: span {[2, -3]} , but how?

I do not necessarily disagree with reply #2.
However, the point is on the line
That line contains , so its direction vector is .

Thus in traditional vector geometry its equation is

So notation is everything here. Unless you tell us about the notation in use in your notes, we cannot really answer.