2) Let V=R²³: W= { x = (X₁₁ X ₂₁ X 3) ER ³²: 2x₁ - x₂ + 5*3=0}. Prove that W is a subspace and find complimentary subspace. Is it (complementary subspace) unique?

Q: rove that W2 = {(a,b) E R² : a = 26²} is not a subspace of R?.

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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 (X, F) be a space. Prove that a subspace of a subspace is a subspace of (X, F).

A: Here given X, I is a topological space.

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: B 1 Find the dimension of the subspace V span{v1, v2, V3, v4} in R³ where vị = 2 1 V2 = , V3 = and…

A: We find dimension of the subspace V

Q: 4: Let H1 and H2 be two subspaces of R". Show that H1 n H2 is also a subspace of R".

A: To show a set W to be a subspace of the of a space X if a,b∈W then a+b∈W   and for a scaler λ and…

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: Q: Let W, ={(a, B.Y, 8): a=y+28, y= 28} and W2 {(a, B.Y, 8):a-y-0} be two subspaces of V,(R). Find a…

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Q: Let S be a subspace of R" and let S be its orthogonal complement. Prove that S- is also a subspace…

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Q: a Let H = :a – 76 + 3c – d = 0}. First show that H is a subspace of M2×2. Then determine dim(H). d

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Q: Consider the subspaces U = {(x,x) | x ≤ R} and W = {(0, y) | y ≤ R} of R². Show that U + W is a…

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Q: If V is a linear subspace of R", and x1 , ×2 , ... , Xn E V, then we must have span {x1, X2, Xn} =V.…

A: To determine that the statement, if V is a linear subspace of ℝn and x1, x2,....,xn∈V, then spanx1,…

Q: Question 3. Let (X,r) be a topological space and YCX. Show that if the subspace (Y,r,) is connected,…

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Q: Find the closest point to y in the subspace W spanned by v₁ and v₂. y = 5 - 1 1 18 V₁ 1 - 2 - 1 3 V2…

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Q: True or False. Justify your answer. Let U Span{1+x, x+x²} and W = Span{x²} be subspaces of P2 (R).…

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Q: If V is infinite-dimensional and S-is an infinite-dimensional subspace, must the dimension of V/S be…

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Q: b) Is W = {f(x):f is a polynomial with degree <3,f (0) 0} a subspace of P: all 3 ? Explain your…

A: To see if the given subset is a subspace of the vector space of all polynomials of degree less than…

Q: Determine the following is the subspace in R’? W ={(x,y,z):x+y+z=0}

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Q: (3) Is Mmxn(Q) is a vector subspace of Mmxn (R) over R?

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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: Let (R, Tus) be the real line.Let r ∈ R such that 0 ≤ r < 1 and consider I = [0, 1] as a subspace of…

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Q: c) Find dimension of subspace of all vectors in R° whose first and third entries are equal.

A: We have to find the dimensions

Q: 2t 6. Let H be the set of all vectors Show that H is a subspace of R³. What is the -t dimension of…

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Q: Prove that the the solution to the equation 2x – y+z= 0 is a subspace of R³.

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Q: Let V= R3 and W= {x:x = a(1; 0; 2) + b(1; –1;3)}, where a and b can be any real numbers. Is W…

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Q: Let S = {E} " +=0}. such that ₁ + X2 + X3 = Either prove that S is a subspace, or find a…

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Q: 2

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Q: c) Determine whether W = {(a, b, c, d) E R*| ad – bc = 0} is a subspace of R*. %3D

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Q: X1 - X₂ = 0 = 0 X3 X4 = 0 X2 - 2x3 -

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Q: Let W = { |xy <0}. Is W a subspace of R?? If so, use generic terms to demonstrate the necessary…

A: W is not a subspace of R2.