- #1
eyehategod
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W={(x1,x2,x3):x[tex]^{2}_{1}[/tex]+x[tex]^{2}_{2}[/tex]+x[tex]^{2}_{3}[/tex]=0} , V=R^3
Is W a subspace of the vector space?
from what i understand for subspace to be a subspace it has to have two conditions:
1.must be closed under addition
2.must be closed under multiplication
so...
I pick a vector s=(s1,s2,s3) and a second vector t=(t1,t2,t3).
for the addition i get:
s+t=(s1+t1,s2+t2,s3+t3)//so its closed under addition
for multiplication i get:
cs=c(s1,s2,s3)=(cs1,cs2,cs3)//closed under multiplicartion
what i don't understand is how the condition x[tex]^{2}_{1}[/tex]+x[tex]^{2}_{2}[/tex]+x[tex]^{2}_{3}[/tex]=0 would come into play. how do i use this condition in this problem?
Is W a subspace of the vector space?
from what i understand for subspace to be a subspace it has to have two conditions:
1.must be closed under addition
2.must be closed under multiplication
so...
I pick a vector s=(s1,s2,s3) and a second vector t=(t1,t2,t3).
for the addition i get:
s+t=(s1+t1,s2+t2,s3+t3)//so its closed under addition
for multiplication i get:
cs=c(s1,s2,s3)=(cs1,cs2,cs3)//closed under multiplicartion
what i don't understand is how the condition x[tex]^{2}_{1}[/tex]+x[tex]^{2}_{2}[/tex]+x[tex]^{2}_{3}[/tex]=0 would come into play. how do i use this condition in this problem?
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