## Elementary Linear Algebra 7th Edition

$$[x]_S=\left[ \begin {array}{ccc} 1\\ -3\\ 0\end {array} \right].$$
Since we have $$x= (1,0,0)-3(0,1,0)+0(0,0,1),$$ then the coordinate matrix of $x$ in $R^3$ relative to the standard basis is $$[x]_S=\left[ \begin {array}{ccc} 1\\ -3\\ 0\end {array} \right].$$