# Chapter 4 - Vector Spaces - 4.7 Coordinates and Change of Basis - 4.7 Exercises - Page 210: 3

$$[x]_S=\left[ \begin {array}{ccc} 7\\ -4\\ -1\\ 2\end {array} \right].$$

#### Work Step by Step

Since we have $$x= 7(1,0,0,0)-4(0,1,0,0)-(0,0,1,0)+2(0,0,0,1),$$ then the coordinate matrix of $x$ in $R^3$ relative to the standard basis is $$[x]_S=\left[ \begin {array}{ccc} 7\\ -4\\ -1\\ 2\end {array} \right].$$

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