Why isn't R2 a subspace of R³?

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

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Q: 3. Determine whether the given set is a subspace of M2x2 with real entries. {6 ) la = b}.

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Q: CLOBE1-2: What is the dimension of the subspace W = {pEP3 such that p(0) = p(1)}? A. Equals 1 B.…

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

A: Explanation of the answer is as follows

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: Q3 Give an example of a connected subspace of R2 which is not path- connected.

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Q: Determine whether the subspaces are orthogonal.

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Q: Determine whether H is a subspace of M22. Give reasons! -X IX H={A€ M22 : A = 0 2x

A: Set of all 2*2 matrices denoted by M22 forms a vector space. We have to determine whether H is a…

Q: answer true or fa 18. R is a subspace of R.

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Q: 3. State why W = {x = (x1, 2, X3, T4) E R' : a1 + x2 + x3 + a4 < 1} is not a subspace of R. (H.W)

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Q: For subspaces V & V*of R° and V±R³, consider the set Š=VUV+. Is 3=R*? (always justify your answer to…

A: No! It's not true that S=R5.See the counter-example below.

Q: What is a linear subspace?

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Q: Determine: If W = the set of all vectors in R2 whose second component is the square of the first. is…

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Q: (() 2 6. Are the two subspaces span and span (() orthogonal? Justify your answer.

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Which of the following subsets of R3x3 are subspaces of R³×3?

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Q: Q;:Is W={A€ M3(R): a11+a22+a33=1} a subspace of M3(R)?.

A: Note :- A subset S of a vector space is said to be subspace iff  1.S is closed under vector addition…

Q: Determine whether W = {(a,2,b)|a,b ∈ R} is a subspace of R^3.

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

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Q: Determine whether W is a subspace of V

A: Given

Q: subspace W of R2.

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Q: S = {[a _b c]€R³|c = ab} _is a subspace of R3. صواب İhi

A: We have to solve given problem:

Q: E M2x3 is a subspace of M3-

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Q: 11. Explain why the subset of R² shaded below is not a subspace of R². 3 1 -3 -2 -1 -1 -2 -3 12.…

A: I have given the details below

Q: Show whether each of the following is a subspace. Justify your answer.

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Q: A base of the subspace W={ (a, b, c); a-2b+c=0} is:

A: According to the question,

Q: Show that W = {a + bx² € P₂|a, b = R} is a subspace of P2.

A: The solution is given as

Q: Discuss what it means to be a subspace and what is required to prove that something is a subspace.…

A: Concept:

Q: Q6: Explain whether the following sets are not subspaces of R" for the appropriate value of n. a a a…

A: We have to show that given set are vector subspace or not

Q: Give an example of a two-dimensional subspace of P3.

A: To give an example of a two - dimensional subspace of P3.   Definitions:             Let V be…

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: Which of the following subsets of RX3 are subspaces of R³x3

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Q: АT (Ь — Ах) — ӧ. Interpret this statement in terms of the fundamental subspaces of A.

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Q: S= {[a b c]e R°|c = ab} is a subspace of R³. صواب İhi

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Q: Determine whether W is a subspace of V

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Q: Is (x > 0, y < 0) a subspace? Explain.

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Q: Explain why the subset а —b S : a + b а,b€ R -2b — За of R³ is or is not a subspace of R³.

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Q: 6. Is the following a subspace? Show/prove which step fails. {x e R? : x1 + x2 = 3}

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Q: CLO3E1-2: What is the dimension of the subspace W = {PEP3 such that p(0) = p(1)} ? %3D A. Equals 1…

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Q: a² a³] а a2 | la is real is a subspace of M3x3 · If it is, prove it; if it is not, Determine if S =…

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Q: Give an example of a two-dimensional subspace of R4 .

A: Consider two-dimensional subspace of R4 is, u1=1111, u2=110-2

Q: S = {[a _b c] e R*|c = ab} is a subspace of R³. صواب İhi

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Q: Select one: O a. a subspace of M_2x2 with dimensic O b. a subspace of M_2x2 with dimensio O c. not a…

A: a) Given set is W=a-b-aa; a,b ∈R This shows that W is a non-empty subset of M2×2

Q: H is not a subspace of R.

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Q: a + 2b a + 1 3. Is H = a subspace of R? Why or why not? a

A: We need to determine if H=a+2ba+1a is a subspace of ℝ3 For a set W to be a subspace of a vector…

Q: L: R3 → R² and L(x) = (2x1 – x2, X2 + x3). Show that ker(L) is a subspace of R3

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Q: Determine: if W = the set of all vectors in R^2 whose second component is the square of the first.…

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Q: What is the dimension of the subspace 0 2 3 1 H = x1 x2 x3 X4 ER¹ : 2x1 3x2 + 4x3 5x4 = 0 ?

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Q: :) Find the subspace of values that balances the chemical equation in which glucose ferments to form…

A: Solution -  We have given equation in which glucose ferments to form alcohol and carbon dioxide.

Q: S= {[a b c]eR* |b = 0} is a subspace of R'. ylgn Ihi O

A: I have proved the basis definition of subspace

Q: is a subspace of M23-

A: A nonempty subset W is a subspace of a vector space V if, whenever w1, w2 are elements of W and α is…