Two vectors are linearly independent if one is not a scalar multiple of the other. To be more precise, two vectors are linearly independent if and only if the matrix A = [u v] whose columns are the vectors u and v has exactly 2 pivots.
Can anyone help me solve this question with workings:
1. Can u= [1,2,-1], v=[2,k2,k] be linearly independent for any k?
Thanks, would really appreciate any help-it is my last question and I'm stuck.
Two vectors are linearly independent if one is not a scalar multiple of the other. To be more precise, two vectors are linearly independent if and only if the matrix A = [u v] whose columns are the vectors u and v has exactly 2 pivots.