Chapter 6.3, Problem 38E

Finding the Image Two Ways In Exercises $37-42$, find $T\left(v\right)$by using $\left(a\right)$the standard matrix and $\left(b\right)$the matrix relative to $B$and $B^{\prime }$.

$T:R^3\to R^2$, $T\left(x,y,z\right)=\left(x-y,y-z\right)$, $\text{v}=\left(2,4,6\right)$,

$B=\left\{\left(1,1,1\right),\left(1,1,0\right),\left(0,1,1\right)\right\}$, $B^{\prime }=\left\{\left(1,1\right),\left(2,1,\right)\right\}$