Let V be the vector space of all functions from  the real field R into R. Show that the set   W={f:f(7)=2+f(1)} is not a subspace of V.

Q: 3. Show that the set W = {(x, 0) : x e R} is a subspace of R?.

A: In order to show W is a subspace of R2 , we need to prove W is closed under addition. For any two…

Q: Determine whether W = {a + 2x + bx²|a, b = R} is a subspace of P2.

A: Explanation of the answer is as follows

Q: Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

A:

Q: Let V be the vector space of all functions from the real field R into R. Show that the set W = {f:…

A:

Q: Let V be the vector space of all functions from R  into R; let V\index{e} be the subset of even…

A: Let V be the vector space of all functions from R into R. and                Ve  = { f(x)  :  f(-x)…

Q: Let H = {[ 21 12 x1, x2 € R 1,2 Show whether or not H is a subspace of R3.

A: We satisfy the clouser and scaler multiplication and show that 0 vector is also in H so H is a…

Q: If W₁ and W₂ are subspace of a vector space V(F), then show that W₁ + W₂ is also a subspace of V(F).

A: W1 and W2 are the subspace of a vector space BF We have to show W1+W2 is also a subspace of BF

Q: f W1 and W2 are subspace of a vector space V(F),  then show that W1+W2 is also a subspace of V(F)

A: Given that W1 and W2 are two subspace of a vector space V over a field F.

Q: Show that {f in C[a,b]:f(a)=f(b)} is a subspace of C[a,b].

A:

Q: The set S of all functions f such that f'(1) = 0 is a subset of the vector space F of all functions…

A:

Q: Let W be a subspace of a vector space V. Show that if x is in both W and W+, then x = 0.

A: Solution is given below

Q: Let P3(R) denote the R-vector space of real polynomials of degree 2 or less p=a+bX+cX2, where a, b,…

A: Given the polynomial .Let the subspace of  be .The subspace is the set of all polynomials from  such…

Q: Define a function f : C -> C by f(x+iy) = (x+2y) + i(3x+4y) for x,y in R. Show that f is additive…

A:

Q: Let V be the vector space of real-valued functions on R. Let H be the set of all linear equations;…

A:

Q: 3x3 Define T:R → R² by T 12 xi + 6x2 Find a non-zero vector in the kernel of T.

A:

Q: Consider polynomials with degree less than or equal to n. We can think that each polynomial…

A:

Q: F1 = {all smooth functions f(t) such that f(0) = 1}. %3D %3D Is F1 a subspace of F?

A: In order to solve this problem you need to know the following notions:

Q: Let T be a linear operator on a two-dimensional vector space V. Prove that either V is a T-cyclic…

A: Let T be a linear operator on a two-dimensional vector space V.The objective is to prove that either…

Q: 1. Determine whether w - {[:]•r:a-4-0} X1 E R? : : x1 – 23 = X2 is a subspace of R?.

A:

Q: Let u and v be nonzero orthogonal vectors in R3. Find bases for the range space and null space of…

A: To find: To find the bases for the range space and null space using the given function f: ℝ3→ℝ3,…

Q: Produce an example of an element of Co (R, R) which is not an element of the following vector…

A: Correct answer is f(x)= Sin(x) which is infinitely many times continuously differentiable but it is…

Q: Prove that the set ? = {(a + b, a -b): a and b are real numbers} is a subspace of ℝ2 with the…

A:

Q: Determine whether W is a subspace of V

A: Determine whether W is a subspace of V

Q: Consider the vector space 2 with the inner product rgk)=x+1,then %3D

A:

Q: a Q#01:- Let W be the set of all vectors in R3 of the form where a and La + b! b are any real…

A:

Q: (a) Let F be a finite dimensional subspace of an inner product space X. Then show that X=F+ F-and F…

A:

Q: be the vector space of all polynomials of degree 3 or less in the variable z. Let PI(T) 2+x+1²,…

A: In this question, we check the given set forms a basis or not. Then we use elementary transformation…

Q: Let U be a subspace of a finite-dimensional Prove that dim(U) = dim(V) if and only if U = V. vector…

A:

Q: Show that the subset of real functions f such that f(0) = 0 is a subspace of F(R) with the usual…

A:

Q: Show that the set T= {(a, b, c, d): 2a-3b+Sc-d=0} is a subspace of R'.

A: Given T=abcd∈ℝ4:2a-3b+5c-d=0 Let A be a 1×4 matrix defined by: A=2-35-1 Then the equation…

Q: Let & denote the vector space of all functions &: R&R under the usual operations of function…

A: B=sint, cost is a basis of H