Let {u₁, U₂, U3, U4} be the orthogonal basis for R¹ given below. Write x as a sum of two vectors v₁ and v₂ with v₁ in Span{u₁, U₂, u3} and v₂ in Span{u}. Enter your answers as 4x1 arrays into v_1 and v_2. x = -8 U₁ = 6 0 U₂ = 2 -6 U₂ = U₁ =

Q: In 3-D, let L be a line that does not pass through the origin. let v1, v2, and v3 be three vector…

A: We have to decide there vectors v1, v2, v3 are linearly indipendent in R3 or not.

Q: Give an example of a set of nonzero vectors in R3 that generates R3 but is not a basis for R3.…

A: Definition 1 : A basis β for a vector space V is a linearly independent subset of V that generates…

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: 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: Find the vector projection of v = -6i + 10j – konto w = = 2i + j − k (Give your answer using…

A: The given two vectors are  v=-6i+10j-k  and w=2i+j-k

Q: Consider the basis B of R² consisting of vectors (-1, 2) and (-6, -3). Find x in R² whose coordinate…

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Q: Consider the space P2 and consider the vectors B ={ 1 + 2t +2t2, 3+5t +3t2,-2-3t} and C = {1,t,t2}.…

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Q: Need help with orthogonal vectors.

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the vector X (in standard coordinates) determined by the given coordinate vector [X] and the…

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Q: Find the coordinate vector of (-1, 32) relative to the basis {(1, 3), (-1, 4)}.

A: We use the definition of coordinate vector relative to a given basis to answer the given question.

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: Find a vector orthogonal to both v = 8 -6 and w 9 0 -6

A: Step 1: The cross product of two vectors is orthogonal to both of the original vector Step 2: Step…

Q: linearly independent If they are linearly dependent, find scalars that are not all zero s linearly…

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Q: Are the vectors = [−5_3 −1], v = [02-1] and w = [-25 21 -8] linearly independent? Choose If they are…

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Q: Consider the points C(3,-2,0), D(-1,5,-1). Let b be the vector with representation CD. Write b in…

A: Ans:

Q: Determine if the vectors vị = (1, –1,3, –1), v2 = (1, –-1, 4, 2), v3 = (1, –1,5, 7) are linearly…

A: We have to determined the vectors v1=(1, -1, 3, -1), v2=(1, -1, 4, 2), v3=(1, -1, 5, 7) are linearly…

Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

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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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