Question

Determine by inspection whether the vectors are linearly independent. Justify your answer.
[4 1], [3 9], [1 5], [-1 7]
Choose the correct answer below.
A.The set is linearly dependent because at least one of the vectors is a multiple of another vector.
B. The set is linearly independent because at least one of the vectors is a multiple of another vector.
C. The set is linearly dependent because there are four vectors but only two entries in each vector.
D. The set is linearly independent because there are four vectors in the set but only two entries in each vector.

Answer 1

Answer:

B. The set is linearly independent because at least one of the vectors is a multiple of another vector.

Step-by-step explanation:

A set of n vector of length n is linearly independent if the matrix with these vectors as column has none of zero determinant. The set of vectors is dependent if the determinant is zero. In the given question the vectors have no zero determinants therefore it is linearly independent.