[理工] [線代]正交補空間問題
今天唸到正交補空間的題目，有兩個問題想請神手幫忙一下
黃子嘉老師的線性代數下冊
Q1.
例61,p7-103
Find a basis for R^3 that includeshte vector
[1] [0]
[0] and [1]
[2] [3]
Ans: 老師上面是並沒有說到W是subspace
考卷上是否要寫上去呢?不然R^3=W⊕W┴不能說得過去...
Q2.
例67,p.7-109
Let W be the subspace of R^4 containing all vectors with
x1+x2+x3+x4=0 and x1+x2-x3-x4=0
find a basis for the space W┴.
Ans:老師上面給的是{(1,1,1,1),(1,1,-1,-1)}
而我用其他方法算出來是{(1,1,0,0),(0,0,1,1)}
不知我的answer是{(1,1,0,0),(0,0,1,1)}
謝謝
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