Find all subrings of z7
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Find all su of z7
1. In Z7[x], find q(x) and r(x) such that 53 1 (22r )r(a) and deg r(x) < 2. 1. In Z7[x], find q(x) and r(x) such that 53 1 (22r )r(a) and deg r(x)
2. Consider Z7 Prove that the operation on Z7 dened by [x]7 [y]7 = [5xy]7 is well dened. = 2. Consider Z- Prove that the operation ♡ on Z- defined by [2]7 0 [y]; [5xy]7 is well defined.
(b) Consider the initial value problem -2 1 z7) = 3 Find ö(t), writing your answer as a single vector.
Please be clear but don't make things complicated 1 in Z7[] (3) Consider x2 + 1 and x2 (a) Show that x2 + 1 is irreducible and that x2 (b) Show that both Z7[x]/(x2 1) and Z7x]/(x2 - 1) have 49 elements. (c) Show that Z7[x]/(x2+1) is a 1 is not irreducible field, but Z7 x/(x2 -1) has zero divisors 1 in Z7[] (3) Consider x2 + 1 and x2 (a) Show that x2 + 1 is irreducible and that...
What are the elements if Z6 and Z7. Based on the elements and the order of the elements which elements of Z6XZ7 have an order of 14. Explain.
Find the flux integral SSs curl(Ē).d5, where F(x, y, z) = [2 cos(ny)+22 +22, 22 cos(z7/2) – sin(ny)e24, 222]T and S is the surface parametrized by F(s, t) = [(1 – 51/3) cos(t) – 4s, (1 – 51/3) sin(t), 5s]T with 0 <t< 27,0 < s < 1 and oriented so that the normal vectors point to the outside of the thorn.
At least one of the answers above is NOT correct. (1 point) Let K Z7, the field of integers modulo 7.(You can read about fields in Chapter 1.8 of the textbook). Consider the vector space P2 of polynomials of degree at most 2 with coefficients in K Are the polynomials 4x2 + 3x + 3, 2r2 + 5x + 4, and 5x2 + 2x + 5 linearly independent over Z linearly independent If they are linearly dependent, enter a non-trivial...
(2) Consider the following groups: Z24; Z3 x Z7 x Z2; Z2 x Z2 x S3; Zg x Z3; G-symmetries of the squareZ. Which of these groups are isomorphic to one another? (2) Consider the following groups: Z24; Z3 x Z7 x Z2; Z2 x Z2 x S3; Zg x Z3; G-symmetries of the squareZ. Which of these groups are isomorphic to one another?
Let F49 be the field of 49 elements constructed in class. The definition of this field is F19={la(x)]F: a(r) e Z,a}} where Z7]is the ring of polynomials in r with coefficients in the field Z7 and a(x)p = {a(x)+ (1]zz + [4],)5(x) : 5(#) e Z7(a]} and addition is given by [a(r)]F+ [b(r)]F = [a(r) + b(2)]F and multiplication is given by [a(r)]F[b(x)]F = [a(z)b(1)]p. 1. Let Fa9t represent the ring of polynomials with coefficients in F9 (a) Show that...