Let W be the subspace spanned by u, and uz. Write y as the sum of a vector in W and a vector orthogonal to W. 13 2 - 1 y = 3 u, = 2 U2 3 14 - 1 4 ..... O A. В. 2 - 11 2 15 y = 10 7 10 13 + y = - 8 20 OC. D. 2 11 4 9 y = 10 - 7 y = 20 - 17 8 12 + L. +

Q: Let W be the subspace spanned by u, and u2. Write y as the sum of a vector in W and a vector…

A: y = 1828u1 = 10-1u2 = 212

Q: 3 0 -6 and u3 = 1 . Note that u₁ and u₂ are orthogonal. It can be shown that u3 is not in the…

A: We have u1 and u2 are orthogonal, we have to construct a non zero vector v that is orthogonal to…

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: The set of which vectors is a basis for A+B Hint: A+B= [aí az a b b2 ba

A: Given A=spana1→, a2→,a3→ , B=spanb1→, b2→,b3→ where, a1→=1,2,0,-1 a2→=0,2,-1,1 a3→=3,4,1,-4…

Q: Select all possible vector equations for the line through the points (1,1,1) and (3,4,5). OF (t) =…

A: Note that the vector equation of the line passing through two points a→ and b→is given by:…

Q: 1 1. Let ui = u2 = 2 and u = U3 -5 Let Wi = Span{u, u2} and W2 Span{u3, u4}. %3D (a) Show that the…

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Q: Determine whether the following sets are subspaces of R³. Realize number 4 as the span of a…

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Q: Let V₁ = 1 -1 3 4 Choose the correct answer below. 11 10 and w= 4 1 9 Is w in the subspace spanned…

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Q: 8 UH⠀⠀ 5 10 Let v₁ = 1 -1 Choose the correct answer below. and w= 5 5 Is w in the subspace spanned…

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Q: Determine whether each collection of vectors is linearly independent or linearly dependent. Justify…

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Q: a2 E R³ are subspaces of R³? (No justification necessary.) Which of the following sets of vectors аз…

A: Vector subspace : A subset W of a vector space V  over the scalar field K is a subspace of V if and…

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: Let W be the subspace spanned by u₁ and u2, and write y as the sum of a vector in W and a vector…

A: Let W be the Subspace Spanned by u1 and u2,Write y as the sum of a vector in W and a vector…

Q: 2. Determine if the following sets of vectors are linearly independent. Then determine if they form…

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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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Q: 3. Find the set of vectors in R³ which are orthogonal to both (4, 2, 0) and (3,6,9).

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Q: Consider the vector v = (1, 6, -1) in R. Let W be the subspace of R consisting of all vectors of the…

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Q: 7. u = (2, 2), v = (2, −2) 8. u = (2,-2), v = (−2, 2)

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