1.7 Linear Independence

Question 1

v1 - v9 are linear independent iif

Answer 1

(a) the vector equation has only one trivial solution
(b) none of the vectors are combinations of the others
(c) Ax = 0 has only one trivial solution
(d) columns of matrix A has a pivot in every column

Question 2

If vectors are not linearly independent….

Answer 2

…then they are linearly dependent. This means that(at least) one of the vectors is a linear combination of the rest.