## Elementary Linear Algebra 7th Edition

$\textbf{0}=(0,0,0,0)$.
Since the zero vector, $\textbf 0$, has the property that $$u+\textbf{ 0}=u,$$ then the zero vector of the vector space $R^4$ can be calculated as follows; Let $\textbf{0}=(a,b,c,d)$ be the zero vector of $R^4$, then for any vectro $(x,y,z,w) \in R^4$, we have $$(x,y,z,w) +(a,b,c,d)=(x,y,z,w) .$$ By comparing the components in the above equation we find that $\textbf{0}=(a,b,c,d)=(0,0,0,0)$.