Assume {u1, U2, us} spans R³.Select the best statement.A. {U1, U2, us, u4} spans R³ unless u is the zero vector.B. {U1, U2, us, u4} always spans R³.C. {U1, U2, us, u4} spans R³ unless u is a scalar multiple of another vector in the set.D. We do not have sufficient information to determine if {u₁, u2, 43, 114} spans R³.OE. {U1, U2, 3, 4} never spans R³.F. none of the above

1. Given: {u1,u2,u3} spans R3. - This meansu1,u2,u3 form a basis for R3, so they are linearly…

Answered: Assume {u1, U2, us} spans R³. Select…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.1: Vector In R^n

Problem 27E: Determine whether each vector is a scalar multiple of z=(3,2,5). a v=(92,3,152) b w=(9,6,15)

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Determine whether each vector is a scalar multiple of z=(3,2,5). a v=(92,3,152) b w=(9,6,15)
2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 = 3 + 2x + 5x². pi i. -9-7x - 15x² ii. 6+11x + 6x² = iii. O iv. 7 + 8x + 9x² b. Suppose that vi = = (2, 1, 0, 3), v₂ = (3, −1, 5, 2), and №3 = (–1, 0, 2, 1). Which of the following vectors are in span {1, 2, 3}? i. (2, 3, -7,3) ii. (0,0,0,0) iii. (1,1,1,1) iv. (-4, 6, -13, 4)
Let u be a linear combination of {1₁, 1₂, 13). Select the best statement. OA. {U₁, U₂, U3, U4} is a linearly dependent set of vectors unless one of {1₁, 12, 13} is the zero vector. OB. (U₁, U₂, U3, U4} is always a linearly dependent set of vectors. OC. {U₁, U₂, U3, U4} could be a linearly dependent or linearly dependent set of vectors depending on the vectors chosen. OD. {U₁, U₂, U3, U4} could be a linearly dependent or linearly dependent set of vectors depending on the vector space chosen. OE. {U₁, U₂, U3, U4} is never a linearly dependent set of vectors. OF. none of the above
a. Write the vector (-4,-8, 6) as a linear combination of a₁ (1, -3, -2), a₂ = (-5,–2,5) and ẩ3 = (−1,2,3). Express your answer in terms of the named vectors. Your answer should be in the form 4ả₁ + 5ả₂ + 6ẩ3, which would be entered as 4a1 + 5a2 + 6a3. (-4,-8, 6) = -3a1+a2+2a3 b. Represent the vector (-4,-8,6) in terms of the ordered basis = {(1, −3,−2), (-5, -2,5),(-1,2,3)}. Your answer should be a vector of the general form . [(-4,-8,6)] =
Let u and v be vectors in a Euclidean space. Select the best statement. A. The difference u - v may not be defined. B. The difference u – v is found by adding u to-v. C. The difference u - v cannot be computed by a simple formula. D. The difference u – v is found by adding -u to -v. E. The difference u – v is found by adding u to V. F. none of the above
Let u4 be a linear combination of {u₁, U₂, U3}. Select the best statement. OA. {U₁, U₂, U3, U4} could be a linearly dependent or linearly dependent set of vectors depending on the vectors chosen. OB. {U₁, U2, U3, U4} is never a linearly dependent set of vectors. OC. {U₁, U2, U3, U4} could be a linearly dependent or linearly dependent set of vectors depending on the vector space chosen. OD. {U₁, U₂, U3, U4} is always a linearly dependent set of vectors. OE. {U₁, U2, U3, U4} is a linearly dependent set of vectors unless one of {u₁, U₂, U3 } is the zero vector. OF. none of the above

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