22.设方阵A^3满足A^3-A^2+2A-E=0,证明:A及A-E均可逆.
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/25 05:31:00
![22.设方阵A^3满足A^3-A^2+2A-E=0,证明:A及A-E均可逆.](/uploads/image/z/7065876-12-6.jpg?t=22%EF%BC%8E%E8%AE%BE%E6%96%B9%E9%98%B5A%5E3%E6%BB%A1%E8%B6%B3A%5E3-A%5E2%2B2A-E%3D0%2C%E8%AF%81%E6%98%8E%3AA%E5%8F%8AA-E%E5%9D%87%E5%8F%AF%E9%80%86.)
22.设方阵A^3满足A^3-A^2+2A-E=0,证明:A及A-E均可逆.
22.设方阵A^3满足A^3-A^2+2A-E=0,证明:A及A-E均可逆.
22.设方阵A^3满足A^3-A^2+2A-E=0,证明:A及A-E均可逆.
A^3-A^2+2A=E
A(A^2-A+2)=E所以A可逆
A^3-A^2+2A-2E=-E
A^2(A-E)+2(A-E)=-E
(A^2+2)(A-E)=-E
(-A^2-2)(A-E)=E所以A-E可逆
22.设方阵A^3满足A^3-A^2+2A-E=0,证明:A及A-E均可逆.
设方阵A满足A^3-A^2+2A-E=0 ,证明: A及A-E均可逆.
设4阶方阵满足|3E+A|=0 ,AAT=2E,|A|
设4阶方阵满足|3E+A|=0 ,AAT=2E,|A|
设方阵A满足A²+3A-2E=0,证明方阵A+3E可逆,并求A+3E的逆矩阵.
设方阵A满足2A^2+A-3E=0证明3E-A可逆
线性代数中,设方阵A满足A^2-2A+3E=0,如何证明 A-3E可逆.
设方阵A满足等式A^2-3A-10E=0,证明A-4E可逆.
设N阶方阵A满足A^2-A-3I=0,怎么得出A-I可逆
设方阵A满足A2(平方)-3A-2E=0,求(A-E)(-1次方)=?
设4阶方阵A满足/A+3E/=0,AA^T=2E,矩阵/A/
设4阶方阵A满足条件:| 3 I +A | = 0,AAT= 2I,| A | < 0,求A*的一个特征值.RT
设4阶方阵|A|=2,求|3A|
设方阵a满足e-2a-3a^2+4a^3+5a^4-6a^5=0证明e-a可逆
设方阵A满足A^2-6A+8E=0,且A转置=A,试证A-3E为正交矩阵
设方阵A满足A^-3A+I=0 试证A可逆
设n阶方阵a满足a^2-2i=0,试证方阵a-i可逆还有
设n阶方阵A满足:A^2+2A-3E=0,证明:R(A+3E)+R(A-E)=n