Homogeneous Definition and 405 Threads

Hi, Please bear with me, I've only had the first sort of "pseudo-lecture" in ordinary d.e.'s this past week, and I was doing some reading ahead. It occurred to me that if linear first-order differential equations are those that can be written in the general form: \frac{dy}{dx} + P(x)y =...

Hi, i have a question. Hope you guys can help~ Ques: Give a geometric explanation of why a homogeneous linear system consisting of 2 equations in 3 unknowns must have inifinitely many solutions. What are the possible numbers of solutions for a nonhomogeneous 2 x 3 linear system? Give a...

Is Cosmos Homogeneous, Isotropic ? Is the universe really homogeneous and isotropic? The answer is hidden within the structure of spacetime.

Can someone explain what the homogeneous equation is :redface: and how do you find the 'null vectors' and hence the general solution. Eg. AX = [6] [8] [4] A = [1 2 4] [3 1 2] [0 2 4] X = [2] [0] [1] Find the null vectors of A and general solution.

Hello all! I'm taking a look at Meserve's "Fundamental Concepts of Geometry" for an introduction to the world of geometry. Section 1-7, A geometry of number triples completely confunded me. It introduced homogeneous points, and in my opinion it either a) did a horrible job, or b) did a horrible...