设A为n阶方阵,且（A-E)可逆,A^2+2A-4E=0.证明(A+3E)可逆,并求(A+3E)^-1
人气：425 ℃ 时间：2020-01-25 18:40:17
解答
证明∶∵A＋2A－4E＝0,∴A＋2AE－3E－E＝0,∴A＋2AE－3E＝E,∴﹙A－E﹚﹙A＋3E﹚＝E,∴﹙A＋3E﹚可逆,且﹙A＋3E﹚﹙﹣1﹚＝A－E
推荐
- 证明题 设N阶方阵A满足A²-2A-4E=0 证明A-3E 可逆
- 设方阵A满足A^2-2A+4E=O,证明A+E和A-3E都可逆,并求他们的逆矩阵
- 设A为N阶方阵,且A-E可逆,A^2+2A-4E=0,求A+3E的逆方阵
- 设A为n阶方阵,满足A^2=3A,证明：（1）4E-A可逆；（2)如果A不等于0,证明3E-A不可逆.
- 设n阶矩阵A满足A^2+2A–3E=0,证明A+4E可逆,并求它们的逆.
- It's none of my business.just get out of my face
- 1.——don't you remember what we have agreed on?we agreed to be here before 6 o'clock
- People ___ ___tea to Europe until the sixteenth century.
猜你喜欢
