Determine if w = -5 is in NulA where A = 2 5 13 21 23 8 14 19 2 O Yes, w is in NulA because Aw is the zero vector. O Yes, w is in NulA because w is in R³ and Nul Ais a subspace of R³. O No, w is not in NulA because w can only be in R³. O No, w is not in NulA because Aw is not the zero vector. 27 1

Q: 10 -00-0 7 12 5 -8- Are the vectors 6 and linearly independent? Explain! 8

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Q: V4. Consider the following two sets of Euclidean vectors: 3x + 2 y + 4 z = 0 y? + 3 x = 3 z Explain…

A: The solution is given as

Q: Consider V = R^3 and U consists of those vectors each of whose first component is non-negative.…

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Q: 2 Let L be the line in R³ that consists of all scalar multiples of the vector . Find the orthogonal…

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Q: 2. Determine whether the following sets with the corresponding vector addi- tion and scalar…

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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: False/True: If vectors V1, V2, ..., Un span the subspace V, then every vector in V can be written as…

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Q: Prove that the set of vectors of the form (a, b, c) where b = a +c is a subspace of R³.

A: According to the given information, it is required to prove that:

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

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Q: Compute the Binary distance between vectors [2, 1, 0] and [8, 5, 0].

A: Given vector points are (2, 1, 0) and (8, 5, 0)  Let (x1 , y1 , z1 ) = (2, 1, 0) And (x2 , y2 , z2 )…

Q: 5 Suppose that u = 1 2 and v= 0 are vectors in R³. Determine the smallest 2 --- 2 subspace H of R³…

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Q: 2. Let y and u = Write y as a sum of two orthogonal vectors, one in Span{u} and a vector orthogonal…

A: y and u are given to us and we need to write y as a sum of two orthogonal vectors such that one is…

Q: Suppose v1, ..., vn are linearly independent and Span({v1, .., vn}) = V , then if W ⊂ V and W…

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Q: 4.) Are vectors Linearly independent? 2 3

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

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