||v||=8 & \(a+45^{\circ}=>a=8\cos45^{\circ}=8*\sqrt{2/2}\)

\(=4\sqrt{2}\) &

\(b= 8\sin45^{\circ}=8*\sqrt{2}/2=4\sqrt{2}=>\)

\(v=4\sqrt{2i}+4\sqrt{2j}\)

Question

asked 2021-02-25

\((u,w)+(u',w')=(u+u',w+w')\ and\ k(u,w)=(ku,kw)\)

(This space V is called the external direct product of U and W.)

asked 2020-11-30

Consider \(\displaystyle{V}={\cos{{\left({x}\right)}}},{\sin{{\left({x}\right)}}}\) a subspace of the vector space of continuous functions and a linear transformation \(\displaystyle{T}:{V}\rightarrow{V}\) where \(\displaystyle{T}{\left({f}\right)}={f{{\left({0}\right)}}}\times{\cos{{\left({x}\right)}}}−{f{{\left(π{2}\right)}}}\times{\sin{{\left({x}\right)}}}.\)

Find the matrix of T with respect to the basis \(\displaystyle{\cos{{\left({x}\right)}}}+{\sin{{\left({x}\right)}}},{\cos{{\left({x}\right)}}}−{\sin{{\left({x}\right)}}}\) and determine if T is an isomorphism.

asked 2021-01-15

asked 2021-05-01

eliptic cylinder

circular paraboloid

hyperbolic paraboloid

plane

circular cylinder