作者juan19283746 (小阮)
看板Grad-ProbAsk
标题[理工] [线代] 内积空间
时间Wed Sep 15 21:36:16 2010
题目:
[ 1 2] [3] T
Let A = [ 2 4] and b= [2] . Find a vector p such that b-p属於N(A )
[-1 -2] [1]
(一个3*2的矩阵)
给的解答:
T
令W=R(A) 取p=proj b 则b-p属於N(A )
w
(b在W上的投影)
T T
欲求p 先解 A Ax=A b
[ 6 12][x1] = [ 6] => [x1]=[1-2*x2]
[12 24][x2] [12] [x2] [ x2 ]
[ 1 2] [ 2]
取p=A[1-2*x2] = [ 2 4]*[1-2*x2] = [ 2]
[ x2 ] [-1 -2] [ x2 ] [-1]
我的答案:
[ 1] [ 2]
因为 [ 2] 和 [ 4] 不为线性独立
[-1] [-2]
[ 1]
所以令 B= [ 2]
[-1]
T -1 T [ 1]
然後算 p=B(B B) B b = [ 2]
[-1]
想请问这样算的问题错在哪里
这章节的观念蛮弱的
谢谢大家
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1F：→ juan19283746:但我把b令为(1,2,-1) 还是不能喔@@ 09/15 22:25
2F：→ juan19283746:另外 这题解为唯一吗? 09/15 22:25
3F：推 cakeboy:这是唯一解 09/15 23:07