Math Answers

Show that in a finite dimensional vector space V(F) whose basic set is B={x₁,x₂,...xₙ} every vector x∈V is uniquely expressible as linear combination of the vector in B.

In the vector space Vs(Rₙ) let α=(1,2,1), β=(3,1,5), -γ=(3,-4,7) prove that the sub space planned by S={α,β} and T={α,β,γ} are same.

In the vector space Vs(Rₙ) let α=(1,2,1), β=(3,1,5), -γ=(3,-4,7) prove that the sub space planned by S={α,β} and T={α,β,γ} are same.

If p(x) denotes the set of all polynomials one indeterminates x over field F, then show that p(x) is a vector space over F with addition defined as addition of polynomials and scalar multiplication defined as the product of polynomials by an element of F. i.e if p(x)={p(x)/p(x)=a₀+a₁x+...+aₙxₙ...}={∑∞,ₙ₌∞ aₙxⁿ for as ∈ f}.

Define addition and scalar multiplication to prove.

If p(x) denotes the set of all polynomials one indeterminates x over field F, then show that p(x) is a vector space over F with addition defined as addition of polynomials and scalar multiplication defined as the product of polynomials by an element of F. i.e if p(x)={p(x)/p(x)=a₀+a₁x+...+aₙxₙ...}={∑∞,ₙ₌∞ aₙxⁿ for as ∈ f}.

Define addition and scalar multiplication to prove.

Let V be set of real valued continuous function defined as [0,1] such that f(0/3)=2. Show that V is not a vector space over R (reals) under addition and scalar multiplication defined as : (f+g)(x)=f(x)+g(x) for all f,g € V.

(alpha f)(x)= alpha f(x) for all alpha € R, f€V.

Let V be set of real valued continuous function defined as [0,1] such that f(0/3)=2. Show that V is not a vector space over R (reals) under addition and scalar multiplication defined as : (f+g)(x)=f(x)+g(x) for all f,g € V.

(alpha f)(x)= alpha f(x) for all alpha € R, f€V.

What's is mathematics