Linearly independent

Is it possible that vectors ${\bf v}_1$, ${\bf v}_2$, ${\bf v}_3$ are linearly dependent, but the vectors ${\bf w}_1={\bf v}_1+{\bf v}_2$, ${\bf w}_2={\bf v}_2+{\bf v}_3$, ${\bf w}_3={\bf v}_3+{\bf v}_1$ are…