计算下列矩阵的 [tex=0.571x1.0]rFc/sfAAuCOtzhevhoREeA==[/tex] 次幂, 其中 [tex=0.571x1.0]rFc/sfAAuCOtzhevhoREeA==[/tex] 为正整数:[tex=7.929x4.786]SG13E7iu2HdaLVWfWJMdasNcssnOsnpcSXP9pfv8ZVudX8uBxPyIW+BW1iuKqBWPQy19xF0hvC5K+ZJXm49WVAb1VZdwsjQNiE6Ohf5lij4=[/tex]
举一反三
- 计算下列矩阵的 [tex=0.571x1.0]rFc/sfAAuCOtzhevhoREeA==[/tex] 次幂, 其中 [tex=0.571x1.0]rFc/sfAAuCOtzhevhoREeA==[/tex] 为正整数:[tex=8.286x3.5]QN0fTQbn6M33pU3gx/S2ssRzVqpWUEMlPB1F8em9pxPHPIIzaitaqaXj3OkAP2YhwLgtNTq7mVpRVmzCUDjgMxeK0fRBchQXdLQiPBE6zvU4+B34aF8ZRVS24QkM3V+Y[/tex]
- 证明一个 [tex=0.571x1.0]rFc/sfAAuCOtzhevhoREeA==[/tex] 一循环置换的阶是 [tex=0.571x1.0]rFc/sfAAuCOtzhevhoREeA==[/tex].
- 设矩阵[tex=6.214x2.786]3BT1BgBZQ5uJXxD5dg+w23rrcqKx27L2L0paZLVx73WXeIIWWUv0DsXtkZVz+pR/niymUxW6MuO9YSZQQGhJXg==[/tex]，求[tex=1.214x1.214]954uF65LINdiWcjcrFsUZg==[/tex]([tex=0.571x1.0]rFc/sfAAuCOtzhevhoREeA==[/tex]为正整数)。
- 设 [tex=0.571x1.0]rFc/sfAAuCOtzhevhoREeA==[/tex] 为正整数，证明:[tex=7.286x2.714]WdYFOXfG5nnGW/WgiEfXS7KSJGNH9TOu8OctQH+TBUAmN+2wRfhYp9VdsOm9mviu[/tex].
- 假设[tex=0.786x1.0]b4HkKtHXeHofHX/gJc8Agg==[/tex]是[tex=2.429x1.071]fYRl1cpBZV0k8ULAvI7FIg==[/tex]矩阵，试证：对任意整数[tex=0.571x1.0]rFc/sfAAuCOtzhevhoREeA==[/tex]，都有[tex=7.714x1.5]wiQyS+D4jxoqMG/+eBuXLQOMSIjzFckfsGPR4aGujdk=[/tex].（当[tex=0.571x1.0]rFc/sfAAuCOtzhevhoREeA==[/tex]是负整数时，规定[tex=10.857x1.786]wiQyS+D4jxoqMG/+eBuXLcPLSSGKOnNKFNz4ahU1kLHIxNIgDCUTNuDb3G2FmBvQLnGxwWgC3ZTOjfpAYEo3HQ==[/tex]）.