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decide whether this is a vector space or not

a(x,y,z) = (2ax,2ay,2az)

all the addition axoims hold easily

for the scalar multiplications axioms

for some real scaral a

[tex] a(x,y,z) = (ax,ay,az) \in 2(ax,ay,az) [/tex]

[tex] a(x_{1}+x_{2},y_{1}+y_{2},z_{1}+z_{2}) = a(x_{1},y_{1},a(z_{1}) + a(x_{2},y_{2},a(z_{2}) \in (2ax,2ay,2az) [/tex] this doesnt seem to hold because it would only be possible if the wo vecotrs being added were not distinct.

[tex] (a+b)(x,y,z) = (ax+bx,ay+by,az+bz) \in (2az,2ay,2az) [/tex]

[tex] a(bx,by,bz) = (ab)(x,y,z) [/tex] this would seem t ohold if b was 2... not not anytrhing else? Not sure here?

multiplcation by 1 gives us what we want. so the last axiom holds

i can post hte axioms if u want

my text says it is not a vector space because of the failure of scalara multiplication where i have stated the doubts mysefl. Are those hte valid reasons for that??

a(x,y,z) = (2ax,2ay,2az)

all the addition axoims hold easily

for the scalar multiplications axioms

for some real scaral a

[tex] a(x,y,z) = (ax,ay,az) \in 2(ax,ay,az) [/tex]

[tex] a(x_{1}+x_{2},y_{1}+y_{2},z_{1}+z_{2}) = a(x_{1},y_{1},a(z_{1}) + a(x_{2},y_{2},a(z_{2}) \in (2ax,2ay,2az) [/tex] this doesnt seem to hold because it would only be possible if the wo vecotrs being added were not distinct.

[tex] (a+b)(x,y,z) = (ax+bx,ay+by,az+bz) \in (2az,2ay,2az) [/tex]

[tex] a(bx,by,bz) = (ab)(x,y,z) [/tex] this would seem t ohold if b was 2... not not anytrhing else? Not sure here?

multiplcation by 1 gives us what we want. so the last axiom holds

i can post hte axioms if u want

my text says it is not a vector space because of the failure of scalara multiplication where i have stated the doubts mysefl. Are those hte valid reasons for that??

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