If X is an inner product space, and A is subspace of X, then AL CAO no decision O ACALO A = A++O

Q: (b) If V = R", and U is a subspace of V of dimension m with 0 <m <n, prove that U² = {v € V: B(u, v)…

A: As per our guidelines we are supposed to solve only one problem. For the solution of the first…

Q: 2. Let а — lb +c а S = {[a – b ,b,c € R a a. Show that S is a subspace of M2x2. 31 -2 31 5 b. Is |…

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Q: Let W be the set of all 2 × 2 matrices A = " 2 га b] such that Az = 0, where z = . Is W subspace of…

A: A set W of vector space V over field F is said to be subspace of vector space V if W is itself a…

Q: Let W = {a + bx + cx² + dx³[ c – 3d = 0 } be a subspace of P3. Then the dimension of W is equal to O…

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Q: 2. Let U and W be subspaces of a vector space V such that UUW is a subspace of V. Prove that UCW or…

A: Given that U and W are subspaces of a vector space V such that union of U and W is a subspace of V.…

Q: 2. Determine whether the set W = {(x,y, z)|x + y +z = 0} is a subspace of R3

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Q: Let X be a topological vector space. Prove that: OFor A, BC X, A+BCA+B. ) If Y is a linear subspace…

A: Given X be a topological vector space. Therefore the maps x,y↦x+y and α,x↦αx are homeomorphism. (a)…

Q: If u and v are vectors in R and W is a subspace of R with (u - v) belong to W, then both u and v…

A: If u and v are vectors in R3 and W is a subspace of R3 with (u-v) belong to W, then both u and v…

Q: Determine whether S={a, +a,x+a,x :a, +a, +a, = 0} is a subspace of P.

A: Here S is a subspace of P2

Q: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

A: Given W is a subspace spanned by the u's where y=322-1, u1=1101, u2=-120-1 AND u3=-1011   To Write:…

Q: 10. Let Y = {(x,y,z)| z=-x}. (a) Is Y a subspace of R³? Justify. (b) Is Y a vector space? Justify.

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Q: Determine is Question 2 whether W = W = {(a; z { (a; 2; 6) | α; 6ER} subspace of R

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Q: 14. Let V = R°and W = {(a, b, c) E Vla² + b² = c²}. Is W a subspace of V? If so,what is its…

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Q: (a) Let S and T be subspaces of a vector space V. Show that SUT is again a subspace of V if and only…

A: As per policy I can solve only one question. Please repost other question.

Q: The set S = ( (x.y, 2) ER |2 = 2, x,y,ZER)is a subspace under vector addition and scalar…

A: This question is related to linear algebra topic vector space.

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

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Q: Is the subset V {(x, y, z, w), y = 3z, w = 2x + 1} a subspace of R*? Show the details of %3D your…

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Q: 1 Let U and V be two subspaces of R" such that UCV. Show that dim(U) < dim(V).

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

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 W = {( ):a :a + 2c = 0 and b-d = 0} be a subspace of M22. %3D %3D Then dimension of W is equal…

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Q: If S and T are subspaces of V, then SUT is a subspace. Select one: True False

A: Given S and T are two subspacewe have to check whether S∪T  is subspace or notClearly  S∪T  is…

Q: 3 show that if w is a subspace of fini a dimensional vector space y and dim (W) = dim (V) W = V.

A: This is theorem in vector spaces

Q: Let W = (a + bx+ cx + dx'|a+ b= 0 and c -3d = 0 ) be a subspace of P Then the dimension of W is…

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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: Let  S=span(e1),  T=span(e2) and  W=span(e1+e3) be subspaces of R3.  S is orthogonal to T, T is…

A: Orthogonal Subspace

Q: Consider the following subspaces of R3: U=span[(2, 1, 1), (1, 2, 0)] W=span[(0, 2, 1), (0, 1, 2)]…

A: We have to find dimension of U∩W.

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: 06. Suppose V is an inner product space, and let U,, U, be two subspaces of V satisfying dim (U,) <…

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Q: a Let W ||a,beR}be a subset of V = R², then W is a subspace of V

A: we have to show that given space is subspace of V

Q: Let W = (a + bx + cx2 + dx'| c- 3d = 0} be a subspace of P. Then the dimension of W is equal to O…

A: dim(W) = number of vector in the basis of W.

Q: If u and v are vectors in R and W is a subspace of R with (u + V) belong to W, then both u and v…

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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: If S and T are subspaces of V, then SNT is a subspace. Select one: O True O False

A: Then 0 or additive identity belongs to S and T  Therefore 0 ∈S∩T so that S∩T =∅ Let x, y ∈ S ∩ T…

Q: Consider X = {1, 2, 3, 4, 5} where the topology is {UC X|1 € U}. Find a subspace of X which is…

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Q: If X is an inner product space, and A is subspace of X then A = A+ True False

A: Let A be a subspace of an inner product space X. Then (i) A⊥ is a subspace of X ; (ii) A∩ A⊥ = (0);…

Q: Consider X = {1, 2, 3, 4, 5} where the topology is {U C X|1 E U}. Find a subspace of X which is…

A: Consider the set X = {1,2,3,4,5} where the topology is {U ≤ X : 1 ∈U}. We have to find a subspace of…

Q: Let S = {" E M2xzi a = d and b+c 0 be a subspace of M2x2. %3D Then the dimension of S is equal to: 4…

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Q: In R, let S be the set of all vectors with third component 0. { a S = ER Show that S is a subspace…

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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: 3) Show that the set of all elements of the form (x + 2y,x + 3z, 2x + y + z), where x, y, z E F, is…

A: We have, (x+2y , x+3z , 2x+y+z),where x, y, z € F.

Q: Let W {a + bx + cx2 + dx³| a+b = 0 and c- 3d = 0} be a subspace of P3. %3D Then the dimension of W…

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Q: 1 SROW thet w in not a subspace 3 a Vecíor space V=R, where wis defined

A: According to our company guidelines, in a multiple questions, we can answer only first question.…

Q: If X is an inner product space, and A is subspace of X then A = AL %3D O True O False

A: TRUE

Q: Let p(x) be a polynomial in P4. Let S be the set of all polynomials from P4 with p(0) = 0. Is Sa…

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Q: Let V be the vector space of symmetric 2 x 2 matrices and W be the subspace -4 -3 3 W = span{ -3…

A: There are so many vectors does no belong to W but belong to V.

Q: If B is basis for (x, t) then By = {BnY/BE basis for the subspace topology Ty on y IS 9

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Q: 4) Suppose u, v E V, where V is an inner product space, and ||u|| = |||| = 1 and (u, v) = 1. Find u…

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Q: Given the fa,, az, az} set of a V subspace. Show that if this subset is lineorly independent, the a,…

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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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Q: Suppose U and W are subspaces of V for which UUW is a subspace. Show that UCW or W CU.

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