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## Homework Statement

Show that a line in R2 is a subspace if and only if it passes through the origin (0,0)

## The Attempt at a Solution

Let A set of vectors be the subset of the vector space R2.

What does it implies in context of this problem if it passes through the origin (0,0)? Does it means contain the zero vector?

S = {(x,y)} = (0,0)

addition:

Let u = u1,u2

Let w = w1,w2

u+w = (u1+w1, u2+w2)

for u1+w1,u2+w2 = 0

u1=-w1

if u1=1, w1 = -1

scalar:

k.u = (ku1,ku2)

ku1,ku2 = 0

ku1 = 0 if k = 0

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