Chapter 6.4, Problem 17E

To determine

(a)

To find:

The transition matrix $P$ from $B=\left\{\left(1,1,0\right),\left(1,0,1\right),\left(0,1,1\right)\right\}$ to $B^{\prime }=\left\{\left(1,0,0\right),\left(0,1,0\right),\left(0,0,1\right)\right\}$.

To determine

(b)

To find:

The matrix ${\left[\text{v}\right]}_B$ and the matrix ${\left[T\left(\text{v}\right)\right]}_{B^{\prime }}$.

To determine

(c)

To find:

The matrix $P^{-1}$ and the matrix $A^{\prime }$.

To determine

(d)

To find:

The matrix ${\left[T\left(\text{v}\right)\right]}_{B^{\prime }}$ with two ways.