Let u4 be a linear combination of {u₁, U2, U3}.Select the best statement.● A. {u₁, U2, U3, U4} is a linearly dependent set of vectorsunless one of {u₁, U2, U3} is the zero vector.●B. {U1, U2, U3, U4} is never a linearly dependent set ofvectors.● C. {U1, U2, U3, u4} could be a linearly dependent or lin-early dependent set of vectors depending on the vectorschosen.● D. {U1, U2, U3, u4} is always a linearly dependent set ofvectors.● E. {U1, U2, U3, U4} could be a linearly dependent or lin-early dependent set of vectors depending on the vectorspace chosen.● F. none of the above

The correct statement is:• E. could be a linearly dependent or linearly independent set of vectors…

Answered: Let u4 be a linear combination of {u₁,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let {1₁, 1₂, 13, 14} be a linearly independent set of vectors. Select the best statement. OA. {1₁, 12, 13} could be a linearly independent or linearly dependent set of vectors depending on the vectors chosen. OB. {u₁, U₂, U3} is never a linearly independent set of vectors. OC. {1₁, 12, 13} is always a linearly independent set of vectors. D. none of the above
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Determine if v is in the set spanned by the columns of B. B= 8-3 2 -9 4-7 6-2 4 5 -1 10 V= 12 -11 10 11 GETOP Choose the correct answer below and, if necessary, fill in the answer box(es) to complete your choice. OA. Vector v is not in the set spanned by the columns of B because the columns of B, b,, b₂, and b, are linearly independent. B. Vector v is not in the set spanned by the columns of B because the reduced echelon form of the matrix formed by writing B with a fourth column equal to v is OC. Vector v is in the set spanned by the columns of B because the columns of B span R¹. OD. Vector v is in the set spanned by the columns of B because b₁ b₂+ b3 FV. +
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6. Let ū, ī, and w be vectors. Explain why any linear combination of i and i is also a linear combination of ū, ī, and w.
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