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6. a. Prove that there is a finite field E with 729 elements and provide the quotient ring that is isomorphic to E. b. Draw the lattice of subfields for E.
Solve for a, b and c. Please write clearly.
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9. (20%) System Differential Equations X = [X1 ; X2] Initial condition X1(0)=1, X2(0) = 1 find the solutions X by (a) Laplace transform method (6%) (b) Diagonalization transform method (7%) (c) Elimination method (7%)
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[5] Given x(t) ? Low pass ter
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2as vf :2 VI
I'm lost on part b, please show all work/steps & write
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Please draw a picture and
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Vectors A and B lie in an xy plane. A has magnitude 3.2 and angle 139 relative to +x direction; B has components B--6.48 and By -6.50. What are the angles between the negative direction of the y axis and (a) the direction of A (b) the direction of the product A x B,and (c) the direction of A x B 3.00k?
Let (X, d) be a metric space, and let ACX be a subset (a) (3 pts) Let x E X. Write the definition of d(x, A) (b) (7 pts) Assume A is closed. Prove that d(x,A-0 if and only if x E A.
Let (X, d) be a metric space, and let ACX be a subset (a) (3 pts) Let x E X. Write the definition of d(x, A) (b) (7 pts) Assume A is closed. Prove that d(x,A-0 if...
need help with proving discrete math HW, please try write
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Let A and be B be sets and let f:A B be a function. Define C Ax A by r~y if and only if f(x)f(y). Prove thatis an equivalence relation on A. Let X be the set of~-equivalence classes of A. L.e. Define g : X->B by g(x) Prove that g is a function. Prove that g is injective. Since g...
this is differential equations ch 8 section 2, please write
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Use the methods of section 8.2 to find the general solutions of the given systems of differential equations in the following three problems. 3. = - X - 4y dx dt dy dt = 2x + 3y
this is from differential equations ch8 section 2 please write
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Use the methods of section 8.3 to find the general solutions of the given systems of differential equations in the following two problems. 4. = X-1 dx dt dy dt = -x + 2y