# Thread: Vector Space with Matrix

1. ## Vector Space with Matrix

The set of all 2x1 matrices [x, y] where x < 0, with the usual operations in R2.

How do I show that this set is not a vector space, using the properties of vector spaces? I'm confused on how to work this out with a matrix. It seems like all the properties hold, but I'm just confused. Thanks guys

2. Hello,

It is the same as if it was numbers or whatever. Matrices are considered as vectors.
Check the rules defining a space vector :
- associative. That is [x,y]+([x1,y1]+[x2,y2])=([x,y]+[x1,y1])+[x2,y2]
- commutative. [x,y]+[x1,y1]=[x1,y1]+[x,y]
- addition has an identity element. is there [x0,y0], which belongs to the set, such that [x,y]+[x0,y0]=[x,y] ?

etc...

I think it's not a vector space because there is a problem with the multiplicative law (no identity element)