Harshal posted an Question
July 29, 2020 • 17:03 pm 30 points
  • IIT JAM
  • Mathematics (MA)

Is diagonalizable if and only if let a e m,.(c). a) a-0. then (o b) a-i. e) n-2. d) none of the other three options

is diagonalizable if and only if Let A e M,.(C). a) A-0. Then (o b) A-I. e) n-2. d) None of the other three options

1 Answer(s) Answer Now
  • 0 Likes
  • 5 Comments
  • 0 Shares
  • comment-profile-img>
    Piyush pachauri best-answer

    PFA Minimal polynomial of M is LCM of minimal polynomial of the blocks. That's why m(M) is zero. Rest is easy , suppose there is another polynomial p which annihilate M then it should annihilate A also. which is contradiction as m is minimal polynomial of A.

    cropped6948666654448324281.jpg
  • comment-profile-img>
    Ujjawal vishal

    zero matrix is always diaganolizable(infact only null matrix that is diagonalizable is null matrix) hence a is correct. Suppose n=1 and then A is 1,then check the eigen values ,it will be 1 with multiplicity 2, but we will get only one eigen vector corresponding to eigen value 1 ,hence not diagonalizable, so A=I is incorrect...for n=2 we can take many examole where it will not be diagonalizable

whatsapp-btn

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