Prove that if A € Mnxn (C) is diagonalizable and L= lim A exists, then either L= In or rank(L) < n. 318

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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4. Prove that if A E Mnxn (C) is diagonalizable and L= lim A exists,
then either L = In or rank(L) < n.
m1x
5. Find 2 x 2 matrices A and B having real entries such that lim A™,
318
lim Bm, and lim (AB) all exist, but
m1x
lim (AB) # ( lim A)( lim B¹). I
818
m→∞o m4x
Transcribed Image Text:4. Prove that if A E Mnxn (C) is diagonalizable and L= lim A exists, then either L = In or rank(L) < n. m1x 5. Find 2 x 2 matrices A and B having real entries such that lim A™, 318 lim Bm, and lim (AB) all exist, but m1x lim (AB) # ( lim A)( lim B¹). I 818 m→∞o m4x
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