НЕ a ER and bE R

Q: If V = R is a vector space and let Hbe a subset of V and is defined as H={(a,b,c): a² +b² = 0,c>0}.…

A: To show that H is not a subspace of a vector

Q: Prove that a subset W of a vector space V is a subspace of V if and only if W = ∅, and, whenever a ∈…

A: We need to prove that a subset W of a vector space V is a subspace of V if and only if W = ∅, and,…

Q: Let S = { (x, y, z, w) E R*; x – 2y + w = 0 and 2x + z – w = 0 } . - Prove that S is a subspace by…

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Q: Let V = M2x2. W. (R) = € V : a, b, cER W2(R) € V : a € R then prove that W, and W2 are subspaces of…

A: Necessary condition to be a subspace is: Vector addition property Scalar multiplication property.…

Q: Let U and W be subspaces of a vector space V. 1. Prove that UnW is also a subspace of V. 2. Must U…

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Q: Let W, and W2 be subspaces of a vector space V. Prove that V is the direct sum of W, and W2 if and…

A: First assume that V is the direct sum of W1 and W2  W1+W2=V and W1∩W2=0 We have to prove that each…

Q: Let V be a finite dimensional, complex inner product space and let U be a subspace of V. Suppose v e…

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Q: Let S be the subspace of P3(R) consisting of all polynomials p(r) such that p(0) = 0, and let T be…

A: The given vector space is ℙ3ℝ. The standard basis of the vector space is p1x=1, p2x=x, p3x=x2,…

Q: Let V be a vector space, F a collection of subspaces of V with the following property: If X,Y EF.…

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Q: Let W be a subspace of Rn. Prove that the intersection of W and W⊥ is {0}, where W⊥ is the subspace…

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Q: Let A be a fixed m × n matrix. Prove that the set W = {x ∈ Rn: Ax = 0} is a subspace of Rn.

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Q: Determine whether the set W={(s, t, s + t) : s and t are real number} is a subspace of vector space…

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Q: Determine if the set W of vectors (X1 , X2) in R such that x1² + x2 = 0 is a subspace of R?.

A: We have to determine whether W is a subspace of R^2 or not.

Q: Consider the set Y = [-1, 1] as a subspace of R. Which of the following sets are open in Y? Which…

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

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Q: Let S be the subspace of Rn spanned by the vectors x1, x2, . . . , xk. Show that y ∈ S⊥ if and only…

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Q: Prove that the subspaces of R3 are {0}, R3 itself, and any line or plane passing through the origin.

A: Let S be a subspace for R3   Hence,              If S is the subspace then by definition:…

Q: Determine whether the set A= (x,y,z):x+y%3D3Z is a subspace of R or not?

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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 X =R, and M = (0} , the M is not subspace of R O True O False

A: Subspace of a vector space

Q: Let U and W denote subspaces of Rn, and assume that U ⊆ W. If dim U = n − 1, show that either W = Rn…

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Q: 16. Show that the set V = {(a-2b+c, 3b, c +2a, b-c) | a, b, c = R} is a vector space that is a…

A: as you asked to solve question 16 only:   given: V = {(a-2b+c, 3b, c+2a, b-c) | a, b, c are in R}…

Q: Determine whether the given set S is a subspace of the vector space V. DA. V = R², and S is the set…

A: As per our company guidelines, we are supposed to solve first question for you. Please submit other…

Q: Show that S is a subspace of R2 where S = {x € R²: x=(5k, 10k), k = R}.

A: Given  S = x∈ℝ2 : x=5k, 10k, k∈ℝ. We have to show that S is a subspace of ℝ2.

Q: Show that the set S = {(x, y) in R2 such that x =3y } is a subspace of the vector space R2 NOTE!…

A: That's easy. Have a good day!!!

Q: It can be shown that the set of all polynomials: p(t) on R is a real vector space. dp Is the set {q|…

A: The objectives to show the given set is a subspace

Q: Consider the set S = {(x, y, z) ∈ R3 | x - 2y = z}. (a) Show that S contains the zero vector. (b) Is…

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Q: Let W be the set of all vectors in R of the form ,where a and bare any real numbers. Determine…

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Q: Let W be the set of all vectors in R³ of the form a B b where b = 2, a is any real number and c < 0,…

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Q: (b) Let V be an n-dimensional F-vector space, and let 0 < k < n. If K is a k- dimensional subspace…

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

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Q: Let X = c, the space of all conver gent sequenes and M == (xn) such that , = 0 then M is not…

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Q: Let S be the collection of vectors [] in R² that satisfy the given property. In each case, either…

A: Note: Hi! Thank you for the question, as per the honor code, we are allowed to answer three…

Q: If W, and W, are two subspaces of a vector space V (F) then prove that WinW, is also a subspace of V…

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Q: If S is a set of vectors in an inner product space V(F) then prove that S- is a subspace of V.

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Q: Let W be the set of all vectors of the form Na subspace of R³ 0 2

A: Here given that  vector  [a 0 2]    We know that condition of subspace  w is zero vector belong…

Q: Take z in W", and let u represent any element = is in wt) Take z, and z in w", and let u be any…

A: Introduction: There are two vectors x,y∈Rn, if they are orthogonal or perpendicular x·y=0. Notation:…

Q: Show that the set W = {(x1, 0, x3): x1 and x3 are real numbers} is a subspace of R3 with the…

A: Given: the set W = {(x1, 0, x3): x1 and x3 are real numbers} is a subspace of R3 with the standard…

Q: a+b+2c 2a +2b+4c+d :a,b,c, d e R b+c+d За + Зс + d

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Q: Let H be the set of all vectors of the form 3s . Find a vector v in R3 such that H = Span {v}. Why…

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Q: snip snip

A: Consider the set S=x,y| xy⩾0. Note that 1, 2,  -2, -1∈S. Because it satisfies 1·2≥0   and   -2·-1≥0.…

Q: a) Prove that W = {(a,b, 2a + b)} is a subspace of R. (more space on the next %3D if needed)

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Q: Let S = { (a, b, c) ER° : b = a +c}. Show that S is a subspace of R'.

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Q: {{} } 5. Let W be the subspace of R³ spanned by write j= |3 as the sum of a vector in W and a vector…

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Q: 2. Let W be the subset of R' consisting of all vectors of the form (x, y, z) x= y+z. Prove that W is…

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Q: Prove that the intersection W n U of two subspaces of a vector space V is a subspace of V and prove…

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Q: Let W be a subspace of R". Set w+ = {x € R"|x™w = 0 for each w in W}. Show that W- is a subspace of…

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Q: Let W be a 3- dimensional subspace of R*, then Dim ( WnW) = Оз O 1 O None of these

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