求4*4 matrix的determinant| -t ,0,0,-24|-t,0,0| 1,-t,0,50 |1,-t,0| 0,1,-t,-35| 0,1,-t| 0,0,1,10-t| 0,0,1用编织发做,算出来等于(-t)(-t)(-t)(10-t)-24但是正确答案是t^4-10t^3+35t^2-50t+24
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![求4*4 matrix的determinant| -t ,0,0,-24|-t,0,0| 1,-t,0,50 |1,-t,0| 0,1,-t,-35| 0,1,-t| 0,0,1,10-t| 0,0,1用编织发做,算出来等于(-t)(-t)(-t)(10-t)-24但是正确答案是t^4-10t^3+35t^2-50t+24](/uploads/image/z/11516206-22-6.jpg?t=%E6%B1%824%2A4+matrix%E7%9A%84determinant%7C+-t+%2C0%2C0%2C-24%7C-t%2C0%2C0%7C+1%2C-t%2C0%2C50+%7C1%2C-t%2C0%7C+0%2C1%2C-t%2C-35%7C+0%2C1%2C-t%7C+0%2C0%2C1%2C10-t%7C+0%2C0%2C1%E7%94%A8%E7%BC%96%E7%BB%87%E5%8F%91%E5%81%9A%2C%E7%AE%97%E5%87%BA%E6%9D%A5%E7%AD%89%E4%BA%8E%28-t%29%28-t%29%28-t%29%2810-t%29-24%E4%BD%86%E6%98%AF%E6%AD%A3%E7%A1%AE%E7%AD%94%E6%A1%88%E6%98%AFt%5E4-10t%5E3%2B35t%5E2-50t%2B24)
求4*4 matrix的determinant| -t ,0,0,-24|-t,0,0| 1,-t,0,50 |1,-t,0| 0,1,-t,-35| 0,1,-t| 0,0,1,10-t| 0,0,1用编织发做,算出来等于(-t)(-t)(-t)(10-t)-24但是正确答案是t^4-10t^3+35t^2-50t+24
求4*4 matrix的determinant
| -t ,0,0,-24|-t,0,0
| 1,-t,0,50 |1,-t,0
| 0,1,-t,-35| 0,1,-t
| 0,0,1,10-t| 0,0,1
用编织发做,算出来等于(-t)(-t)(-t)(10-t)-24
但是正确答案是t^4-10t^3+35t^2-50t+24
求4*4 matrix的determinant| -t ,0,0,-24|-t,0,0| 1,-t,0,50 |1,-t,0| 0,1,-t,-35| 0,1,-t| 0,0,1,10-t| 0,0,1用编织发做,算出来等于(-t)(-t)(-t)(10-t)-24但是正确答案是t^4-10t^3+35t^2-50t+24
编织法? 你是说对角线法则?
4阶及以上行列式不适用!
依次作以下变换
r1+tr2+t^2r3+t^3r4 (即第k行的 t^(k-1) 倍加到第1行,k=2,3,4)
=
0 0 0 -24+50t-35t^2+(10-t)t^3
1 -t 0 50
0 1 -t -35
0 0 1 10-t
由行列式展开定理或行列式的定义
= (-1)^t(4123) [-24+50t-35t^2+(10-t)t^3]
= t^4-10t^3+35t^2-50t+24.