4. Let W be the subspace of R³ spanned by w the orthogonal projection of 8- onto W. - (2/3) 1/3 and ₂ (2/3) -48 -4 -48 11 11 -2/3) 2/3 1/3 Which of the following is (d) 7 A -11

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A: Given a vector space V, let W be subset of V , then W is called subspace of V iff If u and v are…

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Q: O Linear subspace L is given by the equations 2r1 + r2 + 3r3 - 14 = 0 = 0 3r1 + 2r2 – 2r4 3r1 + 12 +…

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Q: Please go through each option with explanation

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Q: 11. Find a basis of the following subspace of R4. W = all vectors of the form (a, b, c, d) where a +…

A: To find: Basis of W={(a,b,c,d) | a+b-c+d=0}.

Q: *1. Which of the following are subspaces? Justify your answer in each case. (d) (x € R³ : x² + x² +…

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Q: Find the closest point to y in the subspace W spanned by V₁ and V₂ 2 2 - 1 y= a. 3/6 -2/6 丽··· -1/6…

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Q: Let W be the subspace spanned by the given vectors. Find a basis for W⊥

A: The orthogonal complement of the subspace W is the set W⊥=v∈V : v, w=0 for all w∈W and the…

Q: *1. Which of the following are subspaces? Justify your answer in each case. (d) (x € R³ : x + x + x²…

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Q: . Let u₁ = (1, -2, -1), U₂ = (2, 2,-2), and v = = (0, 0, 1). v is not in the subspace W spanned by…

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Q: Find the orthogonal projection of onto the subspace W of R¹ spanned by projw (v) = 4 > 5 -19 -6 -6…

A: The given vector is v=5-19-6-6. The given subspace W of ℝ4 is spanned by 3413,4-2-40. We know that…

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Q: Find the orthogonal projection of 0 0 -9 0 onto the subspace V of Rª spanned by -1 -1 -1 proj, (v) =…

A: Let V be the vector space spanned by v1,v2,v3,.....vn. The projection of v onto V is obtained as,…

Q: Consider the following vectors! x₁ = x2= 6 x3 =1 16 -5 X=[²] { Ⓒ) are the weckers S [ X₁, X₁, X3z…

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Q: 2. Consider vectors of the form 2y + 5y 4y 3x + + 5z] 2х 8z ,x, y,z are real # - W = -x + 7z y +…

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A: Given that We  have  to  find  the projection from   onto  its  subspace spanned  by  .Let   be…

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Q: #6. Let W be the subspace of R³ spanned by the two vectors (1, – 1,1) and (3, – 2,0). Which one of…

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Q: 5. Let W₁ = equal to (a) 0 and W2 = (b) 1 0 be subspaces of R³. Then dim(W₁ W₂) is (c) 2 (d) 3 V

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A: We have to solve given problem;

Q: 2. Determine which of the following is a subspace of R". (a) {(x1,x2,...X) 1 x = 0} (b) {(x1,…

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Q: Let V₁ = V₁ and v2. 1 -4 , V2' = -2 3 and w= -3 Determine if w is in the subspace of R³ generated by…

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Q: Find the orthogonal projection of onto the subspace W of R³ spanned by projw(7) = = -15] -8 v = -16…

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Q: -6 -0-0-0-8 9 6 Let v₁ = -3 4 3 = 1. Is w in {V1, V2, V3}? Type "yes" or "no". 13 9 and w= 6 10 4.…

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A: We have to find the orthogonal projection of onto the subspace W of R4 spanned by Let v1 = and v2 =…

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Q: - Consider the following 3 vectors (1). 0 V1 V2 = 0 1 , V3 = 0 0 -1 Find a basis of span{v₁, v2, v3}…

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Q: Find the orthogonal projection of v onto the subspace W spanned by the vectors u. (You may assume…

A: To find the orthogonal projection of v onto W: