50 points
>
Time management is very much important in IIT JAM. The eduncle test series for IIT JAM Mathematical Statistics helped me a lot in this portion. I am very thankful to the test series I bought from eduncle.
Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
- CSIR NET
- Mathematical Sciences
Plz solve it
. 77. Let N be a non-zero 3 x 3 matrix with the property N = 0. Which of the following is/are true.? (A) N is not similar to a diagonal matrix. (B) Nis similar to a diagonal matrix. (C) Nhas one non-zero eigenvector. (D) N has three linearly independent eigen- vectorS.
1 Answer(s)
Answer Now
- 0 Likes
- 1 Comments
- 0 Shares
-
![comment-profile-img]()
>
Do You Want Better RANK in Your Exam?
Start Your Preparations with Eduncle’s FREE Study Material
- Updated Syllabus, Paper Pattern & Full Exam Details
- Sample Theory of Most Important Topic
- Model Test Paper with Detailed Solutions
- Last 5 Years Question Papers & Answers
Sign Up to Download FREE Study Material Worth Rs. 500/-
Ujjawal vishal![best-answer]()
If A is a non zero matrix and A^k =0 then A is called nilpotent matrix. And, remember only nilpotent matrix which is diagonalizable, is null matrix. but here N is non zero ,so it is not diagonalizable. so, option a is correct and b is not correct. Clealry, N can't have 3 linearly independent eigen vectors otherwise it would make it diagonalizable which is not true in case of non zero nilpotent matrix. An example attached which shows it can have non zero eigen vectors. we have find eigen vectors at eigen values 0. So, option C ia correct and D is false.