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(b) Solve the set of congruences 2x =1 (mod 5) x=3 (mod 4)

(b) Solve the set of congruences 2x =1 (mod 5) x=3 (mod 4)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 3CEXP
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Solve 3a and 2b with all steps

as its first row. 4 6 ) are algebraic TT (e) The eigen values of over Q. ИТ-003 1 Р.Т.О. For n>3, show that the symmetric group (a) Sn is not cyclic, but can be generated by 2 elements. (b) Solve the set of congruences 2x=1 (mod 5) x=3 (mod 4) Let S be a non empty set. Show that Map (S, S), the set of all mappings from S to S is a monoid. Determine the group kernel of Map(S, S). (c) 13 (a) Evaluate the legendre symbol 997 irreducible (b) representations of D3. Further, write down the character table of D3. Find the invariant factors of Z8 × Z12× Z15. Determine all the (c) Show that L={x"y|n>0} is a regular (a) language. Check 4. (b) 978-81-266-4945-7 is a valid ISBN number. if the ISBN number Let a, ß be complex numbers. Prove that if a+ß and aß are algebraic numbers, then a and B are also algebraic (c) 5. (a) Let F be a finite field. Show that the product of all the non-zero elements of F is --1. 1 has order 3 and -1 (b) The matrix A = therefore it defines a matrix representation of the cyclic group G of order 3. Find a G-invariant, positive definite hermitian 2. 3.
Transcribed Image Text:as its first row. 4 6 ) are algebraic TT (e) The eigen values of over Q. ИТ-003 1 Р.Т.О. For n>3, show that the symmetric group (a) Sn is not cyclic, but can be generated by 2 elements. (b) Solve the set of congruences 2x=1 (mod 5) x=3 (mod 4) Let S be a non empty set. Show that Map (S, S), the set of all mappings from S to S is a monoid. Determine the group kernel of Map(S, S). (c) 13 (a) Evaluate the legendre symbol 997 irreducible (b) representations of D3. Further, write down the character table of D3. Find the invariant factors of Z8 × Z12× Z15. Determine all the (c) Show that L={x"y|n>0} is a regular (a) language. Check 4. (b) 978-81-266-4945-7 is a valid ISBN number. if the ISBN number Let a, ß be complex numbers. Prove that if a+ß and aß are algebraic numbers, then a and B are also algebraic (c) 5. (a) Let F be a finite field. Show that the product of all the non-zero elements of F is --1. 1 has order 3 and -1 (b) The matrix A = therefore it defines a matrix representation of the cyclic group G of order 3. Find a G-invariant, positive definite hermitian 2. 3.
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