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Homework Statement
Find a basis of U, the subspace of P3
U = {p(x) in P3 | p(7) = 0, p(5) = 0}
Homework Equations
The Attempt at a Solution
ax3+bx2+cx+d
p(7)=343a+49b+7c+d=0
p(5)=125a+25b+5c+d=0
d=-343a-49b-7c
d=-125a-25b-5c
ax3+bx2+cx+{(d+d)/2} -->{(d+d)/2}=2d/2=d
(-343a-49b-7c-125a-25b-5c)/2=-234a-37b-6c
ax3+b2+cx-234a-37b-6c
a(x3-234)+b(x2-37)+c(x-6)
basis{x3-234,x2-37,x-6}
dim=3
please check if I m correct or not
and is there a easier way to do it?
also, if
U = {p(x) in P3 | p(7) = 0, p(5) = 0,p(3) = 0,p(1) = 0}
p(x) does not exist?
thanks!
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