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- 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
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Piyush pachauri
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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.
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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
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Deepak singh 1
see attached, option a Is correct