Write x as the sum of two vectors, one in Span {₁,2,3} and one in Span {u4). Assume that {u.....4} is an orthogonal basis for R4. 0 1 6 U₁ = -1 U₂ 57 1 U3 = 1 D 1 -6 U4= 1 7 5 - 1 1 X = 11 -5 4 0

Q: Find the coordinates of the vector (2, -3, 4, -5) relative to the basis (0, 1, 0, -1), (1, 0, -1,…

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Q: state a vector with all non-zero entries which is orthogonal to v⃗

A: Given v vector  Let w vector be orthogonal to v vector  Then w vector . v vector = 0

Q: Show whether or not the set of vectors B = {U, V, W} where U = V = and W = 0 is a basis for R³.

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Q: 123 Write the vector 2 as a linear combination of the vectors 3 4 (6676) 5 4 2

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Q: The graph below shows vectors u, v and w. 5- -5 -4 -3 ν 4 3 2 -2 2 3 -1 W -2 -3 -4 -5 Clear All…

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Q: Write v as the sum of two vectors, one in Span fu,} and one in Span fu2,u3,u4}. Assume that fu1 .u4}…

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Q: Let B={b₁,b₂} be the basis in R2 pictured below. b₂ 0 If the coordinate vectors [11] b₁ a

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Q: Determine whether the set of vectors {(2,-1,3),(4,1,2),(8,-1,8)} form a basis for R3.

A: Consider the vectors : 2,-1,3, 4,1,2, 8,-1,8 To form a basis these vectors, the vectors must be…

Q: Decide whether the vectors [2, 9, -1, 4, 7, 8, 10, 9], [11, 2, 5, -9, 0, 0, -1, 3], [4, 18, -2, 8,…

A: We have to decide whether the given vectors are linearly independent. Then, we can proceed further.

Q: Find a vector perpendicular to (2, −1, 10) and (1, 2, −1)

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Q: 5. Determine whether vectors u =(2,-6,-5), v = (3,8, 18) and w = (8,-6,7) will form a basis for R³.…

A: Basis is very important in linear algebra. A basis set always contains linearly independent vectors…

Q: Find non-zero vectors I and 7 that are both orthogonal to and orthogonal to each other.

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Q: Represent the vector ⟨16,8,−14⟩ in terms of the ordered basis B={⟨5,−2,−2⟩,⟨1,−4,2⟩,⟨−1,−5,3⟩}.

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Q: Show that the vectors (4-3) and (5,2) form a basis CF TR

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Q: Let be the vector with initial point (4, 7) and terminal point (8,4). Express as a linear…

A: The objective of this question is to express the vector v as a linear combination of the standard…

Q: Show that the vectors (1,1,0), (1,0,1), and (0,1,1) generate F3.

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