Linear combinations Definition and 62 Threads

I have two Lie algebras with structure constants f^{a}_{bc} and g^{a}_{bc}, the number of generators being the same (as will become clear). Due to a particular symmetry/construct, I have that the system needs to be valid under g \to af + bg (and a similar transform for g), which leads...

hi there, my book didn't have an example like this so I am not sure what to do to solve it. Please explain how to do it, thanks. Express the following as linear combinations of p1 = 2 + x + 4x^2, p2 = 1 - x + 3x^2, and p3 = 3 + 2x + 5x^2 a.) -9 - 7x - 15x^2

Homework Statement Suppose that f(x) and g(x) are two eigenfunctions of an operator Q^{\wedge}, with the same eigenvalue q. Show that any linear combination of f and g is itself an eigenfunction of Q^{\wedge}, with eigenvalue q. Homework Equations I know that Q^{\wedge}f(x) = qf(x) shows...

Just to clarify these concepts: if a homogeneous system of linear equations with four variables z1, z2, z3, and z4 yields a matrix in reduced row echelon form that defines (as an arbitrary example) the linear equations z1 = z3 + 0.5z4 = t + 0.5s z2 = 2z3 - z4 = 2t - s z3 = t z4 = s...

Hey all, im taking geometry and discrete mathematics at my school. Its a 12 U course. And I am not doing as well as i would like in it. I am at about a 75, annd i want that to be around 85. So I am looking to you guys for some help. If you guys wouldn't mind awnsering a few questions i have...

I remember this from awhile back but can't seem to find any justification. Why is the smallest positive linear combination of two numbers necessarily the GCD of the two numbers?

Linear combinations?? :S Hey, could som1 please explain linear combinations. I copied down the lecture notes but I'm not understanding this example :confused: may hav typo from the note takin Example: Show that each of the vectors w1 = (1, 0), w2= (0, 1) and w3 = (3, 3) are a linear...

struggling with these problems: 1. determine if the following are: i) collinear: A(0, 3, 2), B(1, 5, 4) and C(3, 9, 8) ii) coplanar: A(1, 4, −5), B(2, 12, −8), C(4, 6, − 4) and D(5, 3, −2) i know that TWO vectors are collinear if it is possible to express one as a scalar multiple of the...

The question is to write the following vectors as a linear combination: c) a vector directed at an angle of 45 degrees with a magnitude of square root of 2. d)a vector directed at an angle of 150 degrees with a magnitude of 6. What I tried to do is to find the scalar quantity with the...

Having a lot of trouble with a particular problem in the topic of variance. The problem is: "Suppose you are organizing a game where you charge players $2 to roll two dice and then you pay them the difference in scores. What is the variance in your profit from each game? If you are playing a...

this is quite a classic problem i think but I am having difficulty finishing it off. If we have two stamps of positive values a and b, (greater than 1), what values can be expressed as a linear combination of these 2 stamps. If the stamps have a highest common factor greater than 1, then there...

{1, x, x(x-1), x(x-1)(x-2)} you want to find the linear combinations that will give you 1, x, x^2, x^3 a + a(x) + a(x(x-1)) + a(x(x-1)(x-2)) = 1 a + a(x) + a(x(x-1)) + a(x(x-1)(x-2)) = x a + a(x) + a(x(x-1)) + a(x(x-1)(x-2)) = x^2 a + a(x) + a(x(x-1)) + a(x(x-1)(x-2)) = x^3 I don't...