Assume \(u,v,w\in\mathbb R^n\) are linearly independent. Prove that \[ 2u+v,\qquad u+v+w,\qquad v-w \] are linearly independent.
Three linear combinations of independent vectors are independent
P-UGASAMP-07
- Area
- Prelim
- Seen at
- UGA
- Status
- draft
P-UGASAMP-07
Assume \(u,v,w\in\mathbb R^n\) are linearly independent. Prove that \[ 2u+v,\qquad u+v+w,\qquad v-w \] are linearly independent.