推 LimSinE :其實就是高斯消去法讓第一行變成1,0,0,0即可 03/24 15:35
※ 引述《lilygarfield (好想有個女朋友喔)》之銘言：
: 想請教一下
: 這個原理是怎麼來的？
: http://ppt.cc/HaBl
純粹這個等式的話, 還可以直接證明; 推廣就不知道了...
|a1 a2 a3 a4| 1 |a1 a2a1 a3a1 a4a1|
|b1 b2 b3 b4| = --------|b1 b2a1 b3a1 b4a1|
|c1 c2 c3 c4| (a1)^3 |c1 c2a1 c3a1 c4a1|
|d1 d2 d3 d4| |d1 d2a1 d3a1 d4a1|
\____^
乘以 (-a2) 加上去
1 |a1 a2a1-a1a2 a3a1 a4a1|
= --------|b1 b2a1-b1a2 b3a1 b4a1|
(a1)^3 |c1 c2a1-c1a2 c3a1 c4a1|
|d1 d2a1-d1a2 d3a1 d4a1|
= ...
1 |a1 0 0 0 |
= --------|b1 b2a1-b1a2 b3a1-b1a3 b4a1-b1a4| = 所求
(a1)^3 |c1 c2a1-c1a2 c3a1-c1a3 c4a1-c1a4|
|d1 d2a1-d1a2 d3a1-d1a3 d4a1-d1a4|
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