Let {u1, u2, u3, u4} be a linearly independent setvectors.Select the best statement.O A. {u1, u2, u3} could be a linearly independentO B. {u1, u2, u3} is never a linearly independent set of vectors.OC. {u1, u2, U3} is always a linearly independent set of vectors.OD. none of the abovelinearly dependent set of vectors depending on the vectors chosen.

L.i--> Linearly independent, L.d.--> Linearly dependent

Answered: Let {u1, u2, u3, u4} be a linearly…

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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Determine by inspection whether the vectors are linearly independent. Justify your answer. 300 - 3 5 Choose the correct answer below. O A. The set of vectors is linearly dependent because (Type an integer or a simplified fraction.) times the first vector is equal to the third vector. OB. The set of vectors is linearly independent because (Type an integer or a simplified fraction.) O C. The set of vectors is linearly dependent because one of the vectors is the zero vector. O D. The set of vectors is linearly independent because none of the vectors are multiples of the other vectors. times the first vector is equal to the second vector.
What are the values of h for which the vectors are linearly dependent? HEH O a. The vectors are linearly dependent if and only if h = -1 O b. There are no values of h for which the vectors are linearly dependent, as the vectors are linearly independent Oc The vectors are linearly dependent if and only if h = 2 O d. The vectors are linearly dependent if and only if h = -16 O e The vectors are linearly dependent for all values of h. Of. The vectors are linearly dependent if and only if h = -10 O g. None of the answers is correct O h. The vectors are linearly dependent if and only if h = -3
Suppose a₁, a2, a3, a4, and a5 are vectors in R ³, A = (a₁ | 8₂ | a3 | a | a5), and a. Select all of the true statements (there may be more than one correct answer). 3 A. span{a₁, a2, a3, a4} = R ³ 3 | B. span{a₁, a2, a3} = R³ C. {a₁, a₂} is a linearly independent set D. {a₁, a₂ } is a basis for R ³ 3 | E. {a₁, A₂, A3, A4} is a basis for R F. {a₁, a₂, a3} is a linearly independent set G. {a₁, a₂, a3 } is a basis for R ³ 3 3 H. span{a₁, a₂} R ³ = rref(A) = |I. {A₁, A₂, A3, A4} is a linearly independent set 9 1 0 0 1 0 0 -4 0 -1 1 1 NL 2 2
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 vectors unless one of {u₁, U2, U3} is the zero vector. ● B. {U1, U2, U3, U4} is never a linearly dependent set of vectors. ● C. {U1, U2, U3, u4} could be a linearly dependent or lin- early dependent set of vectors depending on the vectors chosen. ● D. {U1, U2, U3, u4} is always a linearly dependent set of vectors. ● E. {U1, U2, U3, U4} could be a linearly dependent or lin- early dependent set of vectors depending on the vector space chosen. ● F. none of the above
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