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求行列式形如|-a1,a1,0,·········0,0,0||0,-a2,a2···········0.0,0||································||0,00···-an-1an-10||000·············0-anan||111·······
题目详情
求行列式
形如|-a1,a1 ,0 ,·· ·······0,0,0|
|0,-a2,a2···········0.0,0|
|································|
|0 ,0 0 ···-an-1 an-1 0|
|0 0 0 ············· 0 -an an|
|1 1 1 ··············1 1 1| 的行列式
形如|-a1,a1 ,0 ,·· ·······0,0,0|
|0,-a2,a2···········0.0,0|
|································|
|0 ,0 0 ···-an-1 an-1 0|
|0 0 0 ············· 0 -an an|
|1 1 1 ··············1 1 1| 的行列式
▼优质解答
答案和解析
第二列加第一列,第三列加第二列,.如此类推,n+1列加第n列,成”下三角“型,主对角线上元素为：-a1,-a2,...-an,n+1
所以,Dn+1=(n+1)*a1*a2*...*an*(-1)^n
所以,Dn+1=(n+1)*a1*a2*...*an*(-1)^n
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