Chapter 6.3, Problem 39E

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 $B^{\prime }$.

$T:R^3\to R^4$, $T\left(x,y,z\right)=\left(2x,x+y,y+z,x+z\right)$,

$v=\left(1,-5,2\right)$, $B=\left\{\left(2,0,1\right),\left(0,2,1\right),\left(1,2,1\right)\right\}$,

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