Part C
- If f is an entire function and Im f > 0 then
1) Re f is constant 2) f is constant 3) f = 0 4) f' is a non-zero constant - Let C be an n x n matrix. Let V be a vector space spanned by {I, C, C^2, ... C^2n}. Then dim V is
1) n^2 2) 2n 3) at most n^2 4) at most 2n - Let N be a 3x3 non-zero matrix with the property that N^2 = 0. Then
1) N is not similar to a diagonal matrix 2) N is similar to a diagonal matrix
3) N has one non-zero eigen vector 4) N has three linearly independent eigen vectors
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consider a sequence of functions f_n(x) = 1+ nx where, n belongs to set of natural number, x belongs to [0,1]
ReplyDeleteThen,
1. Uniform limit does not exist
2. Point wise limit exists
3. Point wise limit does not exist.
Given a sequence a_n = {sin(pi)}/ n
ReplyDeletethen, the supremum of the sequence
1. is 0 and is attained
2. is 0 but is not attained
If I = [0,1] . Then for x belonging to R, f(x) = dist (x, I) = INF { |x-y|: y belongs to I}
ReplyDeleteThen,
1. f is continuous on R but is non differentiable at x = 0 and 1
2. f is continuous on R but is non differentiable at x = 1
3. f is discontinuous somewhere on R.