Question

Let f: Z6 --> Z2 X Z3 be the function given by f([a]6) = ([a]2,[a]3). (a)...

Let f: Z6 --> Z2 X Z3 be the function given by f([a]6) = ([a]2,[a]3). (a) Show that f is well-defined; that is, show that if [a]6=[b]6, then f([a]6) = f([b]6). (b) Prove that f is an isomorphism.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider the three groups G1 = Z12, G2 = Z6 x Z2, and G3 = Z4...
Consider the three groups G1 = Z12, G2 = Z6 x Z2, and G3 = Z4 x Z3. (The operation is addition in all cases) (a) Find an isomorphism between two of them (b) explain why the third group is different
A random variable X has probability density function f(x) defined by f(x) = cx−6 if x...
A random variable X has probability density function f(x) defined by f(x) = cx−6 if x > 1, and f(x) = 0, otherwise. a. Find the constant c. b. Calculate E(X) and Var(X). c. Now assume Z1, Z2, Z3, Z4 are independent RVs whose distribution is identical to that of X. Compute E[(Z1 +Z2 +Z3 +Z4)/4] and Var[(Z1 +Z2 +Z3 +Z4)/4]. d. Let Y = 1/X, using the formula to find the pdf of Y.
Consider the function F(x, y, z) =x2/2− y3/3 + z6/6 − 1. (a) Find the gradient...
Consider the function F(x, y, z) =x2/2− y3/3 + z6/6 − 1. (a) Find the gradient vector ∇F. (b) Find a scalar equation and a vector parametric form for the tangent plane to the surface F(x, y, z) = 0 at the point (1, −1, 1). (c) Let x = s + t, y = st and z = et^2 . Use the multivariable chain rule to find ∂F/∂s . Write your answer in terms of s and t.
Let T ∈ L(C3) be the operator given by T(z1,z2,z3)=(z1 +z2 −2z3,z1 +z2 −2z3,z1 +z2 −2z3)....
Let T ∈ L(C3) be the operator given by T(z1,z2,z3)=(z1 +z2 −2z3,z1 +z2 −2z3,z1 +z2 −2z3). Find a basis of C3 such that M(T ) is block diagonal with upper-triangular blocks (as guaranteed by 8.29) and write the matrix M(T ) in this basis.
Calculate ∫ ∫S f(x,y,z)dS for the given surface and function. x2+y2+z2=144, 6≤z≤12; f(x,y,z)=z2(x2+y2+z2)−1.
Calculate ∫ ∫S f(x,y,z)dS for the given surface and function. x2+y2+z2=144, 6≤z≤12; f(x,y,z)=z2(x2+y2+z2)−1.
Let f: Z -> Z be a function given by f(x) = ⌈x/2⌉ + 5. Prove...
Let f: Z -> Z be a function given by f(x) = ⌈x/2⌉ + 5. Prove that f is surjective (onto).
5. Prove that the mapping given by f(x) =x^3+1 is a function over the integers. 6....
5. Prove that the mapping given by f(x) =x^3+1 is a function over the integers. 6. Prove that f(x) =x^3+is 1-1 over the integers 7.   Prove that f(x) =x^3+1 is not onto over the integers 8   Prove that 1·2+2·3+3·4+···+n(n+1) =(n(n+1)(n+2))/3.
Given the function f(x, y, z) = (x2 + y2 + z2 )−1/2 a) what is...
Given the function f(x, y, z) = (x2 + y2 + z2 )−1/2 a) what is the gradient at the point (12,0,16)? b) what is the directional derivative of f in the direction of the vector u = (1,1,1) at the point (12,0,16)?
Let F=(x2+y+2+z2)i+(ex2+y2)j+(3+x)k. Let a>0 and let S be part of the spherical surface x2+y2+z2=2az+15a2 that is...
Let F=(x2+y+2+z2)i+(ex2+y2)j+(3+x)k. Let a>0 and let S be part of the spherical surface x2+y2+z2=2az+15a2 that is above the x-y plane. Find the flux of F outward across S.
Let F be the defined by the function F(x, y) = 3 + xy - x...
Let F be the defined by the function F(x, y) = 3 + xy - x - 2y, with (x, y) in the segment L of vertices A (5,0) and B (1,4). Find the absolute maximums and minimums.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT