[線代] Subspace
問題是這樣的
Determine whether the follwing are subspaces of P4
(a) The set of polynomials in P4 of even degree
(b) The set of all polynomials of degree 3
(c) The set of all polynomials p(x) in P4 such that p(0)=0
(d) The set of all polynomials in P4 having at least one real root
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答案是C
我有看前面課本有飯粒提到C選項
是說跟之前測定的方法一樣
都是使用那兩個
if k is a scalar
kp(0)=k*0=0
if p(x) and q(x) are elements of S
(p+q)(0)=p(0)+q(0)=0+0=0 (這邊我覺得有點怪怪的= =可以這樣分開是因為多項式嗎)
所以C選項這樣被證出來
但是其他三個選項我也想用類似方法 但是卻不得其門而入- -
希望版上的大大可以幫忙一下囉
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