Homework Statement
Consider a particle of mass m that carries a charge q. Suppose that the particle is under the influence of both an electric field E and a magnetic field B so that the particle's trajectory is described by the path x(t) for a\leqt\leqb. Then the total force acting on the...
Homework Statement
Let L be the line in R^3 spanned by v1=(1,1,1)
Find a basis (v2,v3) for the plane perpendicular to L, and verify that B=(v1,v2,v3) is a basis for R^3.
Homework Equations
The Attempt at a Solution
I know that if two vectors are perpendicular or orthogonal that...
Given linear transformations S: Rn --> Rm and T: Rn --> Rm, show the following:
a) S+T is a linear transformation
b) cS is a linear transformation
I know that since both S and T are linear transformations on their own, they satisfy the properties for being a linear transformation, which is that...