show that the set of fourth quadrant vectors is not a subspace of R^2 (2-dimension)

Question

unklerhaukus · Answer

dont you need a zero vector?

anonymous · Answer

is zero vector  in fourth quadrant?

unklerhaukus · Answer

im not sure which quadrant the zero vector is in

unklerhaukus · Answer

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anonymous · Answer

Vectors from the fourth quadrant are u = {a,b} where a is from [0, inf] and b is [0, -inf].
Its not a subspace because this
"If u is an element of W and c is a scalar from K, then the scalar product cu is an element of W" is a condition for W to be a subspace.
So you take a vector u from the fourth quadrant and multiplay it with -1. You get a vector that is not in the fourth quadrant therefore its not a subspace of R^2.