Gate Exam

What are the eigen values of the following 2 x 2 matrix?
2 -1
-4 5
(a) -1 and 1
(b) 1 and 6
(C) 2 and 5
(d) 4 and -1

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Gate Other Question

Consider the set H of all 3 x 3 matrices of the type
a f e
O b d
O O c
where a,b,c,d,e and f are real numbers and abcO. under the matrix
multiplication operation, the set H is:
option
(a) a group
(b) a monoid but not a group
(c) a semi group but not a monoid
(d) neither a group nor a semi group A random bit string of length n is constructed by tossing a fair coin n times and setting a
bit to 0 or 1 depending on outcomes head and tail, respectively. The probability that two such
randomly generated strings are not identical is: