2 Let V1 = 2 , V2 = 5 , and V3 = 1 a. Determine if the set {v1, v2, v3 } is linearly independent. b. If possible, find a linear dependence relation among v1, V2, and V3. SOLUTION a. We must determine if there is a nontrivial solution of equation (1) above. Row operations on the associated augmented matrix show that 1 4 20 2 O 25 10 0 -3 -3 0 3 6 0 0 0 O 0D 1 4 Determine if the columns of the matrix A : 1 2 1 are linearly independent. 0 SOLUTION To study Ax : 0, row reduce the augmented matrix: At this point, it is clear that there are three basic variables and no free variables. So the equation Ax : O has only the trivial solution, and the columns of A are linearly ihdahahdent