The subspace of R spanned by the vectors ui = plane passing through the origin. Express w = where wi lies in the plane and w2 is perpendicular to the plane. (,0, –) and u2 = (1, 2, 3) in the form w = wi + w2, (0, 1,0) is a

Q: Suppose U, W,, W, are subspaces of a vector space V. Show that (Un W,) + (UnW,)Cun (W, + W,) Find…

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Q: The subspace of R3 generated by the vectors u1= (4/5, 0, −3/5) and  u2= (1, 0, 1) is a plane through…

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

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Q: a 2. Is the set of vectors of the form a subspace of R? Show your proof

A: **As per our guidelines we are allowed to answer only one question at a time. Kindly please re-post…

Q: Stretched by the vectors v1 = (1,1,1,1), v2 = (1,2,4,5) and v3 = (1, -3, -4,-2) USR Find an…

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Q: Suppose that you wish to find the projection of u = (3,0,6)" onto the subspace W of R spanned by (2,…

A: We will find out the required solution.

Q: Find the distance of the point (1, 7, -9) in R from the subspace of vectors of the form (a, 8a, b).

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Q: Find the orthogonal projection of onto the subspace W of R³ spanned by projw (v) |||| 6 V H 14 2 and…

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Q: Let u1, u2, u3 be given as shown below. Note that u1 and u2 are othogonal but that u3 is not…

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Q: Find the projection of the vector v onto the subspace S. 8. 4 S span 23/2 9. projs V = 11/2

A: Find the projection of vector V.

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: 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: Show that (a,b,c) where c=a+b is subspace of R3

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Q: what is the smallest subspace containing the vectors u, v and w? what is the span of a set of…

A: Span is the all possible linear combination

Q: Let S be a subspace of R with basis B={[0,1,-3], [3,3,0]) The coordinate vector of v=[-15,-20,15]…

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Q: Find the subspace spanned by the three vectors [2 3 1]T, [2 1-5]T, and [2 4 4]T Feuth

A: We will check the  vectors that it is linearly dependent or linearly independent.  If the vectors…

Q: to the subspace W = Span{u1, u2} where 0. Find the distance from the vector y and u2 = -2 O 2 01

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Q: Find a basis for the subspace of R^3: sp([1, -3, 2], [2, -5, 3], [4, 0, 1]). Show your work, and…

A: We find basis of subspace of R^3: sp([1, -3, 2], [2, -5, 3], [4, 0, 1]).

Q: Find the distance from the point x = (1, 3, -2) of R3 to the subspace W consisting of all vectors of…

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Q: Let-{ », :x, y, a, b e R and x - a = y – b}.Is W a subspace?

A: We will use the one step test for vector subspace to check if W is a subspace or not. We know that…

Q: Find the orthogonal projection of v onto the subspace W spanned by the vectors ui

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Q: Consider the subspace spanned by A ---- and 7₂ and the vector = basis {1, ₂}. = 5 9 in this…

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Q: Suppose that S is a subspace in R spanned by all solutions to -x,+3x,3D0. Then its orthogonal…

A: See the detailed solution below.

Q: Find the orthogonal projection of 3 onto the subspace W of R* spanned by 1 1 -1 1 -1 1 1 1 [1] 1 II…

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Q: Show that the set of vectors {(−4, 1, 3), (5, 1, 6), (6, 0, 2)} does not span R3, but that it does…

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Q: Find the orthogonal projection of v onto the subspace W spanned by the vectors ui

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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: Find the projection of the vector v onto the subspace S.

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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: Describe explicitly a linear transformation from V, (R) into V, (R) which has its range the subspace…

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Q: (b) Define subspace and Verify whether is subspace v = {(x,y,2):x,y,2ER² and x-2y+3z = 5}

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Q: Find a basis for the subspace W of Rª orthogonal to {(1, –2,3, 4), (3, –5, 7,8)}.

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: ) Find a linearly independent set of vectors that spans the same subspace of IR" as that spanned by…

A: First we need to write given vectors in matrix form and try to use row reduced echelon form(RREF) :

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 a linearly independent set of vectors that spans the same subspace of R' as that spanned by the…

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Q: Find the projection of the vector v onto the subspace S. -1 1 -1 S = span v = -1 |-2/3 -2/3 projs v…

A: To find the projection of the vector v onto the subspace S, where

Q: (1, 2, 3, 4, 6) and let W be the subspace of R° spanned by {u1, u2}, where u1 (1, 2, 1, 2, 1) and uz…

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Q: Find a linearly independent set of vectors that spans the same subspace of R' as that spanned by the…

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Q: Find the orthogonal projection of 10 onto the subspace W of R° spanned by 9. and 3 -1-10 3 projw (i)…

A: To find  The orthogonal projection of v onto the subspace of W spanned by the given vectors.

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: Let ui = (1, –2, – 1), u2 = (2, 2, -2), and v = (0,0, 1). v is not in the subspace W spanned by u,…

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Q: determine whether the first vector is in the subspace of R3 generated by the other vectors. 1) (1,…

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Q: Explain why S = {(r,y) : x, y € R, x > 0} is not a subspace of R²

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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: Find the orthogonal compliment of the subspace W of 2x2 upper triangular matrices in the vector…

A: Using standard inner product in the space of matrices.

Q: Q2. Check if the following points lies on the subspace U spanned by the vectors = [2 -1 2]', x2 = [0…

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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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