Which of the following subsets is not a vector subspace in the vector space R^3?

Q: (a) {(a, b, c) ER³ | 2a = 3c}. (b) {(a, b, c) ER3 | a = 0, b = 3c}. (c) {(a+b, ab, 2a + b) | a, b R}…

A: (a), (b) , (c), (d)  are subspaces .

Q: Which one of the following is a subspace of the vector space M2 (R) of 2 x 2 matrices? ss (X) the…

A: .

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Q: One of the following subsets of R² is not subspace. Select one: а. X1 S={ X1=2x2} b. S={ ,X1 =X2} C.…

A: We will check that which subset is not a subspace of R2

Q: Please go through each option with explanation

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Q: Why do the set of all polynomials of degree n or less form a vector space, while the set of all…

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Q: can a subspace of R^n have a dimension less than n.

A: Yes , it can be .

Q: The intersection of an arbitary collection of subspaces of a vector space is also a subspace.

A:

Q: Which of the following sets is not a subspace of the space R^3? (a) R^3. (b) Any plane passing…

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Q: Write the equation of a subspace that passes through a point a ∈ R^d and is orthogonal to a given…

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Q: The shape's vector set is a subspace of R3

A: solution :-

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Q: Is it possible to solve it using words like claim as my professor did in his example in other photo?…

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Q: show

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Q: Suppose V is finite-dimensional and U and W are subspaces of V with W^0 ⊂ U^0. Prove that U ⊂ W.

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Q: Show that ℓ^1 is a normed linear space.

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Q: Let vl ་ མ། 2 - - ་ -2 and determine if w is in the subspace of R³ generated by v¹ and v². Show your…

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Q: et aj = (1,3, –2), a2 = (5,1, 4), and b = (6, –9,3). a) Project b onto the line through aj. b)…

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Q: Show that a subspace of a Hausdorff space is Hausdorff.

A: Prove that, a subspace of a Hausdorff space is Hausdorff.

Q: W = (x:x= X1 X2 LX3 where x3 = 5x₁ + 8x2

A:

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Q: Determine whether the given subset is subspace of R^3 W={(x1,x2,x3):x1+x2+x3=0}

A: Let the subset W is given as W={(x1,x2,x3)| x1+x2+x3=0} Determine whether the given subset is…

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Q: Let U₁, U2, U3 – be the following subspaces of Rª U₁={a, b, c, d)=R4| ²b=c; a=d=0}; U2={(a, b, c,…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: (a) Give examples of three distinct vectors vị, v2, vz in the vector space R³ such that vz E…

A: Let v1 = {1,1,1}v2 = {2,3,4}v3 = {1,2,3} Here  v2 = {2,3,4} = {1,1,1}+{1,2,3} = v1+v3

Q: Is the union of two subspaces of a vector space, a subspace. Justify your answer.

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Q: Let P3 is the vector space of polynomials of the degrees3,Consider the polynomials…

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Q: Give example of subspaces of land l?wich are not closed.

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