Chapter 4 - Vector Spaces - 4.7 Coordinates and Change of Basis - 4.7 Exercises - Page 210: 1

$$[x]_S=\left[ \begin {array}{ccc} 5\\ -2\end {array} \right]$$

Since we have $$x=5(1,0)-2(0,1),$$ then the coordinate matrix of $x$ in $R^2$ relative to the standard basis is $$[x]_S=\left[ \begin {array}{ccc} 5\\ -2\end {array} \right]$$