Which of the following subsets of R" with the usual operations of vector addition and scalar multiplication are subspaces? a. W, is the set of all vectors of the form , where x > 0 b. W, is the set of all vectors of the form , where x > 0, y > 0 c. W, is the set of all vectors of the form , where x = 0 Let W be the set of all vectors in R³ of the form where a and b are La + b any real numbers. Verify the theorem

Q: Let V = R' and let H be the subset of V of all points on the line 3x + 4y = 12. Is H a subspace of…

A: let V=IR2   and Let H be the sub get of V of all pts. on the line.…

Q: Let V=R2 and let H be the subset of V of all points on the line 3x - 2y=-6. Is H a subspace of the…

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Q: 5. Find basis for the subspace u- of R for the vector u (1,3, -4). (Here u- means %3D orthogonal…

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Q: Let W be the set of vectors in R* of the form ГЗа + 267 —а — b 3 a + c where a, b, c represent…

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Q: 2. Let H be the set of all vectors of the form (a – 3b, b – a, a, b) where a and b are arbitrary…

A: Let V be a vector space. H is said to be a subspace of V. If  H is a subset of V. H is closed with…

Q: Let V = R'and let H be the subset of V of all points on the plane 5r + 2y + 7z = 10. Is Ha subspace…

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Q: HConsider the vector space R° (over R) and ZcR consisting of vectors z=(z1, z2 z3), with these…

A: Given Z⊂R3, where R3 vector space.z→=(z1,z2,z3)(a) z1=0(b) z1+z2=0(c) z1+z2=1We have to check in…

Q: Let S be defined as S={ a2 ER| 3az = 2 az + a3 }. Show that S is a subspace of R’under the…

A: In the given question we have to prove that  S={a1a2a3∈ℝ3|3a1=2a2+a3} is a subspace of ℝ3 under the…

Q: |Find basis for the set of vectors in R²on the line y = nx. where n is last digit of your arid…

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Q: 4. Orthonormalize S (Gram-Schmidt). 5. Find the projection of v onto W.

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Q: Show that the set of vectors of the form a +b forms a subspace of R3. Find a 2а — b basis for this…

A: Let          W=aa+b2a-b   where a ,b are in R . If a=b=0, then 0→∈W. It implies that W is non empty.…

Q: Find the dimension of the subspace W of R' spanned by set S = {(-1,2,5,0), (3,0,1,–2), (–5,4,9,2)}

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Q: dimension

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Q: Let f be a function in C[-n, 1] with inner product (f, g) = Sf(x)g(x)dx and W be a subspace %3D…

A: Given  C-π, π is the set of real valued continuous functions in the interval -π, π. Let f, g∈C-π, π…

Q: if it was N-{cz,,z,»z,): 2z,-z, = o} Two subspaces of C³ space on field C find MON Then prove that…

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Q: 16 In the vector space R, let u= (1, 2, 3), v -(3, 1, 5), w-(3,-4, 7). Prove that the subspace S…

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Q: Find the orthogonal projection of 4 onto the subspace W of IR' spanned by 1 1 -1 1 1 1 1 projw (7)…

A: I am solving this in step 2

Q: 4) Let W of R4. Find the matrix for the projection onto W, use the matrix to compute the projection…

A: Given that W=span2,1,3,4 So, this can be written as, W=2t,t,3t,4t,t∈R The definition for subspace…

Q: Find the projection of the vector v onto the subspace S. 1 1 1 S = span 1 v = projs v =

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Q: 2 Find the orthogonal projection ŷ of y = onto the subspace 3 -2 W = Span { ui u2 Ex: 1.23 ŷ =

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Q: 1. Let u and v be vectors in a vector space V, and let H be any subspace of V that contains both u…

A: As per guidelines we have to attempt only 1st question.

Q: 26 Let V be the vector space of all 2 x 2 matrices and let W be the set of matrices of the form X -x…

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Q: 3) Find a basis for the subspace of Pz Censistiny of all vectors of the following properties f(tD,…

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Q: i. Produce a set V that is not a vector space. Prove it. ii. Produce a subset W of a known vector…

A: Use Vector space and vector subspace definition to find these examples.

Q: Let V and W be subspaces of R² that are spanned by (3, 1) and (2, 1), respectively. Find a vector v…

A: From the given problem:   v+w=3,5 , V=3,1 & W=2,1   Let,    v=xVw=yW   So,…

Q: 16 In the vector space R, let u= (1, 2, 3), v = (3, 1, 5). w = (3,-4, 7). Prove that the subspace S…

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Q: Let ū be some fixed vector in R" and let S be the set of all vectors in R" that are orthogonal to ū.…

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Q: Let V be a finite dimensional inner product space and let U and W be subspaces of V . Note: parts…

A: Let V be a real vector space in R3 and for any three vectors u,v,w∈V if we can express these three…

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: W is not a subspace of the vector space. Verify this by giving a specific example that violates the…

A: The objective is to prove that w is not a subspace of the given vector space.

Q: Let (V,(*,*)) be an F-inner product space,where F is either R or C. LetU C V be a subspace and let a…

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Q: 1. Is the following set of vectors in R³ linearly dependent: {(1,0, 3), (2, 1, –2), (0, – 1, 8),…

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Q: Is the following set of vectors in R 3 linearly dependent: {(1, 0, 3),(2, 1, -2),(0, -1, 8),(7, 2,…

A: The solution is given as

Q: 3. Is the set of all vectors (x, y) in R2 with the usual addition and scalar multiplication, a…

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Q: W= im T when W is a T-invariant subspace, and V=ker + W. Where V is finite dimentional, when you let…

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Q: 2 Find the orthogonal projection of u = onto the subspace of R spanned by the vectors 3 2 V1 = V2 =…

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Q: Find the projection of the vector v onto the subspace S. S = span 2 projs v = %3D

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Q: 3) Find a basis for the subspace of R that consists of the intersection of the planes X-3Y = 5Z and…

A: This is a problem of vector space.

Q: Let V = R? and let H be the subset of V of all points on the line -3x + 4y = -12. Is H a subspace of…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: Find the orthogonal projection of u = 1 onto the subspace of R³ spanned by the vectors - 3 2 V1 =…

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Q: 1. Is the following set of vectors in R³ linearly dependent: {(1,0,3), (2, 1, –2), (0, – 1,8), (7,2,…

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Q: 34. Let W be a subspace spanned by u₁ = (1, 1, 1) and u₂ = (-2, 5, -3). Write vector.orthogonal to…

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Q: .Is the set of all vectors of the form b. where a and b are any real numbers, a subspace W of R?…

A: Yes, W is a subspace of R^3.

Q: Let U and W be subspaces of R³ for which dimU=1, dimW=2, and UgW. Show that R=UOW.

A: I have shown all the conditions of direct sum of two subspaces

Q: Find the orthogonal projection of u = 1 onto the subspace of R spanned by the vectors 3 2 V1 = V2 =…

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Q: 18. A vector space V is said to be the direct sum of its subspaces U and W, written V = U®W, if…

A: (a)  Given, V=U⊕W and prove that every vector in V is the sum of some vector in U and some vector in…

Q: Let H be a subspace of real space R. In terms of a geometrical definition of H, which of the…

A: Given:

Q: Consider the vector subspaces U, V  ,W ⊆ Rn such that U ⊆ V ⊆ W. If dimU = 5 and dimW = 7, what can…

A: - it always contains a set of 5  linear independent vectors (True) This statement is True. As dim V…

Q: Which of the following subsets of R" with the usual operations of vector addition and scalar…

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Q: Q2/ Find orthogomal basis for subspace generated by the basis A, = (2,2,4,4), %3D A2 = (0,1,3,5) ,…

A: To find the orthogonal basis, use Gram-Schmidt process.  uk→= vk→−∑j=1k-1proj uk→  vk→, where proj…