Let {u₁, 12, 13} be a linearly independent set of vectors. Select the best statement. {u₁, U2, U3, U4} is also a linearly independent set of vectors unless u4 is a scalar multip another vector in the set. (U₁, U2, U3, U4} could be a linearly independent or linearly dependent set of vectors depending on the vectors chosen. {u₁, U2, U3, U4} is also a linearly independent set of vectors unless u4 = 0.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let {u₁, U2, U3} be a linearly independent set of vectors.
Select the best statement.
{U₁, U2, U3, U4} is also a linearly independent set of vectors unless u4 is a scalar multiple
another vector in the set.
(U₁, 12, 13, 14} could be a linearly independent or linearly dependent set of vectors
depending on the vectors chosen.
{U₁, U2, U3, U4} is also a linearly independent set of vectors unless u4 = 0.
{U₁, 12, 13, 14} is always a linearly dependent set of vectors.
{U₁, U2, U3, U4} is always a linearly independent set of vectors.
none of the above
Assume that the space contains at least four linearly independent vectors.
Transcribed Image Text:Let {u₁, U2, U3} be a linearly independent set of vectors. Select the best statement. {U₁, U2, U3, U4} is also a linearly independent set of vectors unless u4 is a scalar multiple another vector in the set. (U₁, 12, 13, 14} could be a linearly independent or linearly dependent set of vectors depending on the vectors chosen. {U₁, U2, U3, U4} is also a linearly independent set of vectors unless u4 = 0. {U₁, 12, 13, 14} is always a linearly dependent set of vectors. {U₁, U2, U3, U4} is always a linearly independent set of vectors. none of the above Assume that the space contains at least four linearly independent vectors.
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