[線代] dimension, rank+nullity problem
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Let V be the vector space, under the usual operations,
of real polynomials that are of degree at most 3.
Let W be the subspace of all polynomials p(x) in V
such that P(0)=P(1)=P(-1)=0. Then dim V + dim W is 5.
我知道dim V =4 b/c basis for V is {1,x,x^2, x^3}
T:W->R(real numbers)
nullity(T)=3 b/c P(0)=P(1)=P(-1)=0
rank(T)=0 b/c T把所有W裡面的多項式送到0
那這樣dim W是4,
total is 9.
為什麼呢>"<
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