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

Determine by inspection whether the vectors are linearly independent. Justify your answer. -6 2 30 3 Choose the correct answer below. O A. The set is linearly independent because the first vector is a multiple of the other vector. The entries in the first vector are - 3 times the corresponding entry in the second vector. O B. The set is linearly dependent because neither vector is a multiple of the other vector. Two of the entries in the first vector are - 3 times the corresponding entry in the second vector. But this multiple does not work for the third entries. O C. The set is linearly independent because neither vector is a multiple of the other vector. Two of the entries in the first vector are - 3 times the corresponding entry in the second vector. But this multiple does not work for the third entries. O D. The set is linearly dependent because the first vector is a multiple of the other vector. The entries in the first vector are - 3 times the corresponding entry in the second…

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

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. +