testion 5 Given the subset 7-((1.-2,1).(-1.2, -1).(-6, 12, -6)) of R. which of the following is the subspace of R' spanned by T Oa SpanT ={(x.y.2) ER'ax + y-2-0 Ob SpanT-((x.y.z) ER'IS -y+z 0 Oc SpanT=1(x.y,z) ERE-x=0} Od. SpanT R a

Q: The set W : 3x - y = z -5w = 0} is a subspace of R*. What is the dimension of W Select one: а. 1 b.…

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Q: 4) Which of the following is a subspace of R^3? Justify your answer. i) W={(x,y,z)|x+y+z=0} ii)…

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Q: Determine if (x, y, z, t) ∈ R^4 such that y = −x and z = 0, and t = 2x form a subspace of R^4

A: Use the necessary and sufficient condition for a subspace of a vector space

Q: Wi = {(a,b,c,d) E R* : a+ b+ c = 0} ve W2 = = 0, b = 0}, Being subspaces of R^4 {(a,b,c,d) e Rª : a+…

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Q: The subspace of R spanned by the vectors ui = plane passing through the origin. Express w = where wi…

A: Let W be subspace of ℝ3 spanned by the vectors u1=45,0,-35 and u2=0,1,0. Let A=x,y,z be a non zero…

Q: Find the orthogonal projection of onto the subspace W of R³ spanned by projw() = 4 6 V= 19 16 and -5

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Q: (b) For subspaces X and Y, the sum X + Y is a direct sum (denoted X + Y) if every VEX + Y can be…

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Q: 6. Determine if {(x, y): x^2 + y^2 ≥ 8} is a subspace of R^2

A: The given set is {(x, y) | x2 + y2 ≥ 8}. We check whether the set is a subspace of R2.  Since the…

Q: For any fixed vector v in R^n, the set V=?x∈R^n :v^(T)x=0 is a subspace of R . Assuming v does not…

A: According to the given information, Let V be a fixed vector in Rn, the set V is given as:

Q: a Let M = . -b a,b,c e R},N x, y e R} be two subspaces of M2x2. Find the basis for M, N and MON.

A: We will find the bases of M and N. Then we will find the intersection of their basis vectors, which…

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

A: Since you have posted a question with multiple sub-parts, we will provide the solution only to the…

Q: Determine whether the given set S is a subspace of the vector space V. DA. V = C5 (I), and S is the…

A: A subset S of vector space V is said to be a subspace of V if it is closed under vector addition and…

Q: The set {(x, , x,)' 1 x,+ x, =0} form a subspace of R Select one: O True False

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Q: What is the dimension of the sum of subspaces V and W in R^4, if V=span{(1,−1,0,1),(1,0,−1,1)} and…

A: Answer is (e) 4Explanation:Step 1: Step 2: Step 3: Step 4:

Q: What is the dimension of the sum of subspaces V and W in R^4, where V=span{(1,−1,0,1),(1,0,−1,1)}…

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Q: The normal line to the surface x² + 2y² + ² = 25 at the point (1, -2, 4) is parallel to the vector O…

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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: 14. Which of the following is a subspace of M2,3? Justify your answer. a C. C a) U = E M2.3 b = ac…

A: The solution is given as

Q: Which of the following are subspace of its (indicated) ambient space? a=20} =1} = { [2₁] =R² : 2₁…

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Q: Show there is no proper five dimensional subspace of R^5. (i.e. If V is a subspace of R^5 with dim…

A: To Show: If V is a subset of ℝ5, with dimV =5 then V=ℝ5.

Q: show what W = {(a,0,b)| a,b E R)  is a subspace of R^3

A: Given : W={(a,0,b)|a,b∈R}   To Show : W is subspace of R3

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Q: The set { n > 1} is closed in (0, 0) as a subspace of R. - True - False I know the answer is true…

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Q: Let V be the subspace of R' spanned by vi = (1, 3, -2, 2, 3 ), v (1, 4, -3, 4, 2 ), v3 (1, 3, 0, 2,…

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Q: Let V = R? and K = R. Which of the following are subspaces of V? Give reasons for your answers.…

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Q: Find a basis for the subspace w of (-co, co) W (f f'+2f- 0} O A. -2x 2e O B. No correct answer OC. O…

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Q: ) Consider C with the usual inner product, given by (u, v) = ₁₁ + The vectors are orthogonal. Let…

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Q: a) Is the set W = {(x, y, 1) | x, y are real numbers} a subspace of R^3 ? (b) Is the set W = {(x,…

A: Subspace test:  Let V be a vector space and W is a subset. The subset W is said to be subspace if it…

Q: [2r+r Let H be the set of all vectors of the form , here, fand rrepresent arbitrary real out 21-r…

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Q: Let H= {*] 1}. * : 8x² + 6y² s which represents the set of points on and inside an ellipse in the…

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Q: Which of the listed sets is a vector subspace of the space V=R^2 over the field R?

A: Look at the below attachment option b satisfies the conditions Explanation:Step 1: Step 2: Step 3:…

Q: 5) For each of the following subsets of F', determine whether it is a subspace of F³ : (where Fis…

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