Consider an algebra where the vector space is ℝ3 and
the multiplication of vectors is the...
Consider an algebra where the vector space is ℝ3 and
the multiplication of vectors is the conventional cross product you
learned as a beginning physics student. Find the structure
constants of this algebra.
A basis of a vector space V is a maximal linearly independent
set of vectors in V . Similarly, one can view it as a minimal
spanning set of vectors in V . Prove that any set S ⊆ V spanning a
finite-dimensional vector space V contains a basis of V .
Define a subspace of a vector space V . Take the set of vectors
in Rn such that th
coordinates add up to 0. I that a subspace. What about the set
whose coordinates add
up to 1. Explain your answers.
In the real vector space R 3, the vectors u1
=(1,0,0) and u2=(1,2,0) are known to lie in the span W of the
vectors w1 =(3,4,2), w2=(0,1,1), w3=(2,1,1) and w4=(1,0,2). Find
wi, wj ?{w1,w2,w3,w4} such that W = span({u1,u2,wk,wl}) where
{1,2,3,4}= {i,j,k,l}.
Let be the surface defined by z=x 2+y 2.a.Find the traces of S in the coordinate planes.b.Find the traces of S in the plane z=k,where k is a constant.c.Sketch the surface S.
Determine whether the set with the definition of addition of
vectors and scalar multiplication is a vector space. If it is,
demonstrate algebraically that it satisfies the 8 vector axioms. If
it's not, identify and show algebraically every axioms which is
violated. Assume the usual addition and scalar multiplication if
it's not identified. V = R^2 , < X1 , X2 > + < Y1 , Y2
> = < X1 + Y1 , 0> c< X1 , X2 >...