Chapter 6.CR, Problem 57CR

Finding the Image Two Ways In Exercises 57 and 58, find $T\left(\text{v}\right)$by using (a) the standard and (b) the matrix relative to B and $B^{\prime }$.

$T:R^3\to R^3$

$\begin{array}{l}T\left(x,y\right)=\left(-x,y,x+y\right),\text{v}=\left(0,1\right)\\ B=\left\{\left(1,1\right),\left(1,-1\right)\right\},B^{\prime }=\left\{\left(0,1,0\right),\left(0,0,1\right),\left(1,0,0\right)\right\}\end{array}$