## Elementary Linear Algebra 7th Edition

$$[x]_{B'}=\left[ \begin {array}{ccc} 2\\\frac{3}{2} \end {array} \right].$$
Writing $x$ as a linear combination of the basis $B'$ as follows $$x=(2,-1)= a(1,1)+b(0,-2).$$ We get the system \begin{align*} a&=2\\ a-2b&=-1. \end{align*} By solving the above system we have the soluiton $$a=2, \quad b=\frac{3}{2}.$$ Thus, the coordinate matrix of $x$ in $R^2$ relative to the basis $B'$ is $$[x]_{B'}=\left[ \begin {array}{ccc} 2\\\frac{3}{2} \end {array} \right].$$