Let V = {f| f: R→ R}. Now, denote by U and W the subsets of V composed of even and odd functions, respectively. A. B. Show that U and W are subspaces of V. Show that V=UOW.

Q: Show that V is not a subspace of R°: V is the set of all (x, y, z) such that x + y +z = 3

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

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Q: Consider the R-vector space V-R2. Which of the following subsets of V is a subspace? The line 2x+y=1…

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Q: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

A: Given W be a subspace spanned by the u's, We have to write y as the sum of a vector in W and a…

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: Let W be the set a of all vectors of the form | 0 [2 Is W a subspace of R³

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Q: Let V be an n-dimensional vector space. Define f: V→ R by f(v) = |v|". Let p,q E V.Find d fp(q).

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Q: Determine whether W is a subspace of V

A: Given: V=M22, W=abcd : ad≥bc. To check: Whether W is a subspace of V or not.

Q: c) Mark each statement True or False. Justify the answer. A subspace is also a vector space. • R? is…

A: Here , A subspace is olso a vector space: it is true.  R^2 is a subspace of R^3 : it is false.

Q: Prove that W1 = {(a,b) E R² : 4a – b= 0} is a subspace of R2.

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Q: Find the dimension of the subspace U={[a+c, b+c, a+2c+b] | a, b, c in R} Select one: a. 2 b. 4 c. 1…

A: We have given a subspace ,  U = a + c , b + c , a + 2c + b / a , b , c ∈ ℝ We need to find dimension…

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…

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Q: b) Let W = { 0) * x, y e R}. Show that W is not a subspaces of M2x2. %3D

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Q: Let W be the set a of all vectors of the form | 0 2 Is W a subspace of R

A: The question is to show whether W is a subspace or not. We show that the sum of two vector does not…

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

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Q: Find all values of h such that vector y will be in the subspace of R spanned by vectors 3. V1, V2,…

A: we will first find the equivalent matrix and then reduce it to row echelon form

Q: Letv be a vector Space and let V Vz rin Vnt V. ret w=span { vi, VE, n VnS. Prove W is a subspace of…

A: A necessary and sufficient condition for a nonempty subset W of a vector space V to be a subspace…

Q: Determine whether U = {(1, s, t)ls,t e R} is a subspace of R.

A: FOR ANY SUBSET U TO BE A SUBSPACE OF ANY VECTOR SPACE V IT IS NECESSARY THAT U HAS ZERO VECTOR IN…

Q: Let W be a subspace of Rn. w ∩ w⊥ = {o}

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Q: .: Remind that the set F of all functions from R to R is a vector space. Prove that the set E of…

A: We know that If W is a subset of a vector space V , then W is a subspace of V if and only if the…

Q: 2. Let H be the set of all vectors of the form claim. 2t 0. Is H a subspace of R³? Show your

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