Recent content by JPanthon

Homework Statement http://people.math.carleton.ca/~mezo/A5math1102-11.pdf number one Homework Equations The Attempt at a Solution What does Z5/5 mean?

Homework Statement f(x) = x^3 [cos(pi/x^2) + sin(pi/x^2)] for x≠0 Homework Equations The Attempt at a Solution I really am stuck. I've tried squeeze theorem on [cos(pi/x^2) + sin(pi/x^2)], but I can't compute the range. So, I tried doing it individually, squeezing -1 ≤...

Thank you so much for your reply! b = <b1, b2, ..., bn> c = <c1, c2, ..., cn> b + c = < (b1 + c1), (b2 + c2), ..., (bn + cn)> We know: Ab = 0 s.t. 0 = Ab1, Ab2, ..., Abn Ac = 0 s.t. 0 = Ac1, Ac2, ..., Acn => Ab + Ac = <(Ab1 + Ac1, Ab2 + Ac2, Abn + Acn)> => A(b+c) =...

Anyone? Please?

Homework Statement It is number three on the following page. http://people.math.carleton.ca/~mezo/A3math1102-11.pdfHomework Equations No idea. The Attempt at a Solution I have no idea how to incorporate the kj. Best I could reason through this is supposing: b1 ∈ N(A) , c1 ∈ N(A) Ab1 +...

Just realized how ugly it looks! Sorry, just ignore the underscores and pretend that they are spaces. Or if you could tell me how to make better matrices on the computer I would be happy to redo my post!

Homework Statement Solve -x1 + 6x2 -2x3 = 0 5x1 + x2 + 2x3 = 0 over Z7 Additional Question: How can we immediately tell there is more than one solution?Homework EquationsDon't know. The Attempt at a Solution [-1 6 -2 0]_________[ (-1mod7) 6 (-2mod7) 0] [5 1 2 0] _____=>...

Homework Statement Thanks to everyone who has helped me so far - I'm very grateful. (1) Prove that the multiplicative inverse in any field is unique (2) Prove the cancellation law | ab = ac => b=c (3) Prove (-1)a = -a Homework Equations The field axioms...

Homework Statement Suppose that δ = min{1,e/7}. Show that if |x - 3| < δ, then |x^2 - 9| < e Homework Equations Don't know. The Attempt at a Solution |x - 3| |x + 3| < e Given : |x - 3| < δ => |x - 3| < e/7 |x + 3| |x-3| < e/7 |x + 3| 7|x - 3| < e Assume δ < 1, =>...

Homework Statement Let p be a prime number. Prove: (a+b)^p modp = [(a^p modp) + (b^p modp)]modp Homework Equations modular arithmetic. The Attempt at a Solution I honestly haven't the slightest clue. Would induction be my best bet here? If so, when I suppose the...

Thank you again. If you would just help me once more. It's this part I don't understand: ((a mod n) + (b mod n)) mod n I understand how I've proven (a+b)modn = a(modn) + b(modn) , but not a(modn) + b(modn) = ((amodn) + b(modn)) modn

Thank you for your reply :) So, "((a mod n) + (b mod n)) mod n" means (a+b) plus an integer times n? Could you help me see this?

Homework Statement Suppose a, b, n are integers with n >/= 2 Prove that: (a + b) mod n = ((a mod n) + (b mod n)) mod n Homework Equations Modular arithmetic rules. The Attempt at a Solution r1 = a(modn) => a = q1n + r1 r2 = bmodn => b = q2n + r2 r1 + r2 = a -...

Oh, I see my mistake. Thank you. I don't really know: I took the reciprocal to try to get d and e in the same form, so I may choose d. Could I have a hint to a more efficient method?

I took the reciprocal of both sides - is that allowed?