Let $v_1=(1,2,1,-1)$, $v_2=(-2,3,8,-3)$, $v_3=(-8,5,22,2)$, $v_4=(1,2,3,0)$, $v_5=(2,3,0,-1)$ be row vectors in $\mathbb R^4$.
- Are row vectors $v_1,v_2,v_3$ linearly independent?
- Are row vectors $v_1,v_2,v_3,v_4,v_5$ linearly independent?
I understand that when vectors are linearly independent, the equation $c_1v_1 + c_2v_2 \cdots + c_kv_k = 0$ holds only when $c_1 = c_2 = c_k = 0$.
Any help would be appreciated.