A为三阶矩阵,E为三阶单位矩阵A的三个特征值分别为1,2,-3,则下列矩阵中是可逆矩阵的是:A.A-E B.A+E C.A+3E D.A-2E 为什么答案是B?

Maria Sharapova
Wimbledon women's singles final will be held this Saturday night passion Beijing staged against both were Russian beauty Maria Sharapova and also the Czech genius Colavito baby. Today, each side have accepted an interview prior to the final, Sharapova admits that she is extremely eager to rediscover the winning feeling the peak period, and never to become outdone Colavito baby also explain their advantages.
Sharapova won his career so far has 3 Grand Slam title, this Wimbledon she seemed to be the first six games to keep a losing, these are her for Sunday's final filled with confidence, Talking about do to prepare yourself for that final, the Russian beauty is extremely relaxed: "Peace Day isn't any various, with no special role to play, I believe I'll sleep a great nap, this is exactly what I need to do to prepare Obviously I wish to win the sport,pink ghd, I'd have said this championship special meaning for me is,buy pink ghd hair straighteners, I wish to rediscover the winning feeling. "Sharapova stated not too long ago compared to their to become more aged, that is easy to face her final essential reason: "I have a big old, more aged psychological aspects of my career recently it's experienced numerous ups and downs, I know how to much more great to face all this, I don't like is individuals who make their own leisurely down, truly, I am very eager to return in the past that winning perspective of field continuously. "
Colavito WTA baby is no doubt the hottest star on the track, get to the last 4 at Wimbledon last year,InStyler Hair Crimping Iron, she went further in his career this year's initial Grand Slam final track, although the final opponent is has three Grand Slam titles and struggle with their own take advantage of Sharapova, but still feel very confident Colavito baby, On this final Sunday when she was bold to point out their benefits where: "Obviously I serve is a big advantage, I love to serve immediately after the attack, and that i love watching men's tennis match,Hair Straightener, Del Potro has been my favorite player, we play much like the , hit the ball very quickly and incredibly flat. "
Colavito also stated he's presently small baby don't really feel nervous, she will 't be in the race for the ear-piercing screams Sharapova feel any be concerned: "I didn't feel any tension, on the contrary I am getting excited about this final I now sleep well and I such as the grass court battle, it can maximize my technical characteristics, so I made a great record. In addition, I don't worry about stadium noise issues, after i entered the race I'd not think about other activities, but simply to focus on their game. semifinal game and that i Azarenka she'll scream, however i don't care,good hair straighteners, I really don't even think it'll bring a lot impact. "

|A|的值为三个特征值的乘积，当|A|不为0，则矩阵的秩为3，可逆
|A-E|=（1-1）（2-1）（-3-1）=0
|A+E|=（1+1）（2+1）（-3+1）不为0，选B

若要A+aE可逆,只需|A+aE|≠0,即a不是-A的特征值,亦即-a不是A的特征值.因此a≠-1,-2,3即可.观察选项,只有A+E可逆,选B.

原因很简单，由Jordan标准化知，A可看作上三角阵，对角线值为1,2,-3.detA=-6.
所以det(A-E)=det(A+3E)=det(A-2E)=0，而det(A+E)=-12