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Math Help - Vector Space with Matrix

  1. #1
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    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
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  2. #2
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    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)
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