## Elementary Linear Algebra 7th Edition

$$[x]_B=\left[ 11 \quad 2 \quad 15\right]^T.$$
Let $x=(5,10,15)$ and $B=\{ (\frac{3}{5},\frac{4}{5},0),(-\frac{4}{5},\frac{3}{5},0),(0,0,1) \}$ To find the coordinates of $x$ relative to $B$, we have to find the following; $$\langle (5,10,15),(\frac{3}{5},\frac{4}{5},0)\rangle = 3+8=11$$ $$\langle (5,10,15),(-\frac{4}{5},\frac{3}{5},0)\rangle = -4+6=2$$ $$\langle (5,10,15),(0,0,1)\rangle = 15.$$ Then, the coordinate matrix of $x$ relative to $B$ is given by $$[x]_B=\left[ 11 \quad 2 \quad 15\right]^T.$$