Chapter 6.3, Problem 37E

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 $B^{\prime }$.

$T:R^2\to R^3$, $T\left(x,y\right)=\left(x+y,x,y\right)$, $\text{v}=\left(5,4\right)$,

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