Express the indicated vector w as a linear combination of the given vectors v, and v, if this is possible. If not, show that it is impossible. 7 4 -4 v, = 3 8 w = 8 7 Select the correct answer below, and fill in the answer box(es) to complete your choice. O A. It is possible to express the vector w in terms of v, and v,, as w = V2. (Type integers or fractions.) O B. It is impossible to express the vector w in terms of v, and v2, because an echelon form of the augmented matrix [v, v2 w], E= is inconsistent. (Type an integer or simplified fraction for each matrix element.) shows that the system

write the following vectors as linear combinations of e1, e2 and e3

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. +

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.