[理工] [線代] 100交大資工
1 2 1 2
8. Consider a matrix A = [ 1 2 2 5 ] and a system of linear equations
0 0 1 3
-1
Ax = b = [ 3 ] . Which of the following vectors c will make the two systems
1
Ax = b + c and Ax = b have the same least-square error.
T
A. c = [0, -1, -1]
T
B. c = [3, 2, 2]
T
C. c = [1, 0, -1]
T
D. c = [2, 1, 2]
T
E. c = [1, 2, 1]
Ans: ACE
我自己的想法是把下面兩式聯立
T T
A Ax = A b .... (1)
Ax = b + c .... (2)
T T T
把(2)帶入(1) => A (Ax) = A (b + c) = A b
T
=> A c = 0
T
=> c = N(A )
1
算出來的結果就是 {[-1 ] s| s belongs to R}
1
囧 跟選項都差十萬八千里
有哪位大大可以指點一下迷津嗎
提示一下方向就好不用太詳細的過程
感激不盡
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