线性代数_例题解-5

例5.计算n阶行列式aax att…ax Xaa…ac x+(n-1aaa…aa axa…aala+e2|x+(m-1)axa…aa C+C 解: aax…a x+(n-1)aax…aa aaa…xaa+cnx+(m-1)aaa…xa la aa a x x+(n-1 a x x+(n-Da a a 72-i 0 x-aa…a 73-l1 0 [x+(n-1)a](x-a) 0 00 X-a d 0 00 -a 上页 结束 下页

上页 结束 下页 例 5 计算 n 阶行列式 a a a a x a a a x a a a x a a a x a a a x a a a a             解 解   a a a a x a a a x a a a x a a a x a a a x a a a a            1 3 1 2 1 c c c c c cn + + +  ===== ( 1) ( 1) ( 1) ( 1) ( 1) x n a a a a x x n a a a x a x n a a x a a x n a x a a a x n a a a a a + −  + −        + −  + −  + −  3 1 2 1 1 r r r r r r n − − −  ===== 0 0 0 0 0 0 0 0 0 0 ( 1) x a x a a x a a a x a a a a x n a a a a a  −  −       −  −  + −  解 a a a a x a a a x a a a x a a a x a a a x a a a a            1 3 1 2 1 c c c c c cn + + +  ===== ( 1) ( 1) ( 1) ( 1) ( 1) x n a a a a x x n a a a x a x n a a x a a x n a x a a a x n a a a a a + −  + −        + −  + −  + −  解 a a a a x a a a x a a a x a a a x a a a x a a a a            1 3 1 2 1 c c c c c cn + + +  ===== ( 1) ( 1) ( 1) ( 1) ( 1) x n a a a a x x n a a a x a x n a a x a a x n a x a a a x n a a a a a + −  + −        + −  + −  + −  3 1 2 1 1 r r r r r r n − − −  ===== 0 0 0 0 0 0 0 0 0 0 ( 1) x a x a a x a a a x a a a a x n a a a a a  −  −       −  −  + −  =[x+(n−1)a](x−a) n−1 