## Elementary Linear Algebra 7th Edition

$$[x]_{B'}=\left[ \begin {array}{ccc} -5\\-11\\ 9 \end {array} \right].$$
Writing $x$ as a linear combination of the basis $B'$ as follows $$x=(4,-2,9)= a(1,0,0)+b(0,1,0)+c(1,1,1).$$ We get the system \begin{align*} a+c&=4\\ b+ c&=-2\\ c&=9. \end{align*} By solving the above system we have the soluiton $$a=-5, \quad b=-11, \quad c=9.$$ Thus, the coordinate matrix of $x$ in $R^3$ relative to the basis $B'$ is $$[x]_{B'}=\left[ \begin {array}{ccc} -5\\-11\\ 9 \end {array} \right].$$