- #1
pyroknife
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The problem is attached.
I'm having problems with parts a and c, well maybe not part a (probably just need to check if I did this part right. I'm just not sure if I'm wording part a right.
Anyways for part a I must prove it's a subspace so I must satisfy 3 conditions:
1) 0 is in S
2) if U and V are in S, then U+V must be in S
3) if V is in S, then fV is in S for some scalar f.for 1)
By inspection if a=b=c=0 then 0 is in S
for 2)
if U is of the form:
a1-b1 a1
b1+c1 a1-c1
and V is of the form:
a2-b2 a2
b2+c2 a2-c2
then U+V=
a1+a2-b1-b2 a1+a2
b1+b2+c1+c2 a1+a2-c1-c2
Thus U+V is in S. <<< Can I say this?
for 3)
fV=
f(a2-b2) f(a2)
f(b2+c2) f(a2-c2)
Thus fV is in S. <<< Can I say this?
For part c, I don't even know where to begin. Can someone give me a hint?
I'm having problems with parts a and c, well maybe not part a (probably just need to check if I did this part right. I'm just not sure if I'm wording part a right.
Anyways for part a I must prove it's a subspace so I must satisfy 3 conditions:
1) 0 is in S
2) if U and V are in S, then U+V must be in S
3) if V is in S, then fV is in S for some scalar f.for 1)
By inspection if a=b=c=0 then 0 is in S
for 2)
if U is of the form:
a1-b1 a1
b1+c1 a1-c1
and V is of the form:
a2-b2 a2
b2+c2 a2-c2
then U+V=
a1+a2-b1-b2 a1+a2
b1+b2+c1+c2 a1+a2-c1-c2
Thus U+V is in S. <<< Can I say this?
for 3)
fV=
f(a2-b2) f(a2)
f(b2+c2) f(a2-c2)
Thus fV is in S. <<< Can I say this?
For part c, I don't even know where to begin. Can someone give me a hint?
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