Recent content by Samuelb88

Thanks for the replies guys but I've solved this problem. In case you were wondering, I needed to find a matrix such that the image of the vector (2,-10,16,2) is the vector (2,-10,16,0). Pretty simple, I was just confused as to what exactly a "gaussian elimination matrix" was. :smile:

Homework Statement If f and g are continuous real functions on [a,b] which are differentiable on (a,b), then there exists a point x \in (a,b) such that [f(b)-f(a)]g'(x) = [g(b)-g(a)]f'(x). The Attempt at a Solution Not sure if my reasoning is correct here... I can assume that closed intervals...

Alright, so here's what I have. Let A = \begin{bmatrix} 1 & -1&2& 3 \\ 0&1&1&-2\\2&1&7&0\\1&2&1&5 \end{bmatrix}. Looking at A^T, and row reducing, I get that the independent columns of A (i.e. the independent rows of A^T) are (1,0,2,0), (0,1,0,0), and (0,0,0,1). Hence the range space of the...

Homework Statement What is the Gaussian elimination matrix for the vector for the vector v=(2,-10,16,2)? The Attempt at a Solution I don't understand the question. What is a "Gaussian elimination matrix for a vector?" I know that Gaussian elimination is a method for solving a system of...

So I believe I understand what you're saying. Construct the matrix A = [x_1 \, \, x_2 \, \, x_3 \, \, x_4 ] . How do I verify it's range? Should I look at the transpose of the matrix A and row reduce, then the nonzero rows will be my linear span of the range of the matrix that I started from?

Let e_1 = (1,0,0,0), ..., e_4 = (0,0,0,1). Then if A is a 4x4 matrix, then the vector A e_1 would be the first column of A, ..., A e_4 would be the fourth column of A. I'm not sure I'm understanding your post. What do you mean when you say the image of A? Edit: I still don't understand what the...

Homework Statement Represent the linear span of the four vectors x_1 = (-1,1,1,2), x_2 = (2,1,7,1), x_3 = (3,-2,0,5), and x_4 = (1,0,2,1) as the range space of some matrix. The Attempt at a Solution It's been along while since I've done any linear algebra and so I'm not sure what to do...

Homework Statement Suppose that on the time interval [0,h] we have a force acting along the x-axis with magnitude 0 \leq f(t) at time t, and f(0) = f(h) = 0. For a particle of mass m starting at rest, so that its distance x(t) from 0 satisfies 0 = x(0) = x'(0), show that x'(h) = \int_0^h f(t)...

Thanks DH and Philip. Can't believe I didn't think of dividing both sides by change in t then letting the change go to zero! Although I probably wouldn't of appealed to the relation p_r'(t) = -p_e'(t).

A real number that is sufficiently small.

I'm reading Spivak's mechanics book and I'm stumped on some of the math in his derivation of an analytic expression for the motion of a rocket in empty space. Let \mathbf{v}(t) be the rockets velocity, let \mathbf{q}(t) be the velocity at which fuel is ejected from the rocket, and let m(t) be...

I dreamed that my girlfriend and I got into a huge argument because she was claiming closed intervals in R weren't compact.

Opps! I would need to use z(t) = \pi/2 + e^{it}, but shouldn't I still be able to apply my theorem to find that the integral is equal to -1/2? Wolfram is still giving me an output of 0.

Homework Statement Let C be a loop around \pi/2. Find the value of \frac{1}{2\pi i} \int_C \frac{\sin(z)}{(z-\pi/2)^3} dz.Homework Equations Thm: If f is analytic in its simply connected domain D, and C is a simply closed positively oriented loop that lies in D, and if z lies in the inside of...

So I've identified the problem. I counted (x,x,y,y) twice.