Re: [理工] [線代]有關維度的問題
※ 引述《jvvbn0601 (part2)》之銘言：
: Let W={(x1、x2、x3、x4)屬於R^4：x1+x2+x3+x4=0，x1-x2+x3-x4=0}.
: Prove that W is a subspace of R^4 and dim(W)=2
: 請問要怎麼做呢?
x1+x2+x3+x4 = 0
x1-x2+x3-x4 = 0
1. 0屬於W
解上式
2(x1+x3) = 0 x1=-x3
2(x2+x4) = 0 x2=-x4
w=span{[1.0.-1.0][0.1.0.-1] w=span[f.g]
dim(W)=2
令p.q屬於W
p=c1f +c2g
q=d1f +d2g
(αp+βq) = (αc1f+αc2g)+(βd1f+βd2g)
=(αc1+βd1)f + (αc2+βd2)g
滿足加法乘法封閉性
故為子空間
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