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. {u₁, U₂, U3} is always a linearly independent set of vectors. OD. none of the above

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. {u₁, U₂, U3} is always a linearly independent set of vectors. OD. none of the above

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

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. +
Q7. Two vectors are defined as A = a,+ 5ay +3a, and B = the following vector is perpendicular to (A+ B) -4a,+4ay 3a,+ 2a, + a,. Which of %D 4ay-7a, ax+ az None of these
Determine by inspection whether the vectors are linearly independent. Justify your answer. 3 -2 0 3 Choose the correct answer below. O A. The set of vectors is linearly independent because (Type an integer or a simplified fraction.) times the first vector is equal to the second vector. OB. The set of vectors is linearly dependent because (Type an integer or a simplified fraction.) 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 third vector.
Let ā = (−1, 1, 3) and 6 = (0, -4, k). a Find k so that a and b will be orthogonal. k =
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
Set B 1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the vertices of a parallelogram. 2. Let Ā and B be nonzero vectors. Find k eR such that Ā - kB is orthogonal to Ā + B.
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