## Elementary Linear Algebra 7th Edition

$$[x]_S=\left[ \begin {array}{ccc} 4\\ 2\\6\end {array} \right].$$
Since we have $$x= 4(1,0,1)+0(0,1,0)+2(0,1,1)=(4,2,6).$$ then we can write $x$ relative to the standard basis of $R^3$ as follows $$x= (4,2,6)=4(1,0,0)+2(0,1,0)+6(0,0,1) .$$ Thus, the coordinates matrix of $x$ in $R^3$ relative to the standard basis is $$[x]_S=\left[ \begin {array}{ccc} 4\\ 2\\6\end {array} \right].$$