Recent content by EWW

Thanks a lot Turin, I'll review your post and work through your example . . . happy holidays, EWW

By "triangle transformation" I mean the affine transformation of 3 points in 2-space. By "synthetically", I mean by ruler and compass- sometimes this method leads to spatial/geometrical insights that I wouldn't have thought of. My goal is to apply mathematical transformations to...

Thanks Turin, I went back and carefully worked out how an affine transformation is composed of a linear transformation and a translation f(v) = l(v) + a. For a triangle, your left with a 2 X 2 matrix plus the translation vector. If you imagine this to be embedded in 3-space you can shift the...

I understand that for the matrix of an affine transformation, if I take a point x, y and send it through the matrix, I get another point, x', y'. For the fixed point of an affine transformation, the two points are equal. For example, with some 2 X 2 matrix with vector columns -2,3 and 5,-4, I...

Hello, I'm having difficulties with finding fixed points of affine transformations. I understand that given a matrix A of barycentric coefficients, I want to produce a point that is equal to the given point, i.e. Ax = y, where y = x. But all I get is a homogenous linear system whose only...

Hello, I've got two homogenous equations: 3x + 2y + z - u = 0 and 2x + y + z +5u = 0. I'm trying to find a basis for these solutions. The solution vector x [x, y, z, u] is a solution if and only if it is orthogonal to the row vectors, in this case a and b ([3, 2, 1, -1], [2, 1, 1, 5)]...

Question on Newton’s Method of solving systems of non-linear equations. I understand the concept for a single non-linear y=f(x) solved for zero, but am confused about systems of non-linears. If I take two functions U(x,y) and V(x,y), am I solving for the points where they intersect with each...

thanks, the equation makes immediate sense to me once I remind myself that sin^2 x + cos^2 x = 1 . . . I will try graphing these because it is still a little strange to me why the constants should be related in some way.

Hello everybody, I've encountered the following problem in Morris Kline's textbook on Calculus (chapter 10, section 5, ex. 2) that I can't seem to understand- if y' = sin x cos x, then if I set u = sin x, then du/dx = cos x (chain rule), then y = (sin^2 x) / 2. If I set u = cos x, then...