Recent content by p3forlife

Hi, I have a question about proofs by contradiction in general. Without getting into the mathematical details, suppose we had the statement: For every (condition A), B is true. If we want to prove this by contradiction, we want to assume the negation of this statement, and then prove it to...

Thanks :) It makes sense.

Homework Statement Describe the phase portrait of the nonlinear system x' = x^2, y' = y^2 Also, find the equilibrium points and describe the behaviour of the associated linearized system. The Attempt at a Solution We have an equilibrium point at (0,0). The associated linearized...

Homework Statement Prove that the integral of sin(t)/t+1 dt from 0 to x is greater than 0 for all x > 0 Homework Equations If f is bounded on [a,b], then f is integrable on [a,b] iff for every epsilon > 0 there exists a partition P of [a,b] s.t. U(f,P) - L(f,P) < epsilon. The...

Homework Statement Prove that the integral of sin(t)/t+1 dt from 0 to x is greater than 0 for all x > 0Homework Equations If f is bounded on [a,b], then f is integrable on [a,b] iff for every epsilon > 0 there exists a partition P of [a,b] s.t. U(f,P) - L(f,P) < epsilon.The Attempt at a...

I'm having trouble finding the inverse of f(x) = x + [x]. I think it comes back to what is the inverse of the greatest integer function, [x]. I have graphed [x], and its inverse is the reflection along the y = x line, which appears to be similar, although the inverse graph is "vertical". Is...

Argh...sorry this is taking so long :S So since L(W) is the set of all linear transformations from W to W, it means that V is a subset of a W, since there is the restriction of T(x1) + T(x2) = T(x4) In L(W), we start off with 16 dimensions, since each of T(xi) for i = 1, 2, 3, 4 has 4...

So L(W) means you take an x in W, you apply a transformation, then you get T(x), where the set of all T(x) is the range of W.

Okay, so finding a basis for L(W)... Since beta = { x1, x2, x3, x4} is a basis for W, if you do a linear transformation from W to W, the basis should be { T(x1), T(x2), T(x3), T(x4)} ? Sorry...I'm striking a blank about this problem.

So the matrix for a general T will look like: [T] = [a11 a12 a13 a14] [a21 a22 a23 a24] [a31 a32 a33 a34] [a41 a42 a43 a44] where a11 + a12 = a14 a21 + a22 = a24 a31 + a32 = a34 a41 + a42 = a44 but i can't get any farther...

Homework Statement Find a basis for V. Let W be a vector space of dimension 4. Let beta = {x1, x2, x3, x4 } be an ordered basis for W. Let V = {T in L(W) | T(x1) + T(x2) = T(x4) } Homework Equations L(W) is the set of linear transformations from W to W The Attempt at a Solution...

Thanks for your reply. So it's obvious that the zero vector is in W. Check if T + S is in W (closure under addition): T(1,0,1,0) + S(0,1,0,-1) = 0 + 0 = 0 Since T + S is in N(T), W is closed under addition. Check if cT is in W (closure under scalar multiplication): cT(1,0,1,0) = c * 0...

Okay, so checking if T(0,0,0,0) = 0 is asking if (0,0,0,0) is in N(T). Since (0,0,0,0) is not in N(T), then the zero vector is not in W. Is this right?

Homework Statement Determine whether the subset W of the vector space V is a subspace of V. Let V = L(Q4) (the set of linear transformations from rational numbers with 4 coordinates to rational numbers with 4 coordinates). Let W = { T in V = L(Q4) | { (1,0,1,0) , (0,1,0,-1) } is contained in...

I have trouble understanding how damping affects the period (of a torsion pendulum). I know that damping affects the amplitude of the oscillator, however how would damping change the period then? I have a feeling this has to do with angular frequency, w, given by: w = sqrt( (k/m) -...