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Consider the following bases and coordinate matrix.

```
B={(4,2,-4),(6,-5,-6),(2,-1,8)}
B^(')={(3,2,120),(1,1,60),(2,2,140)}
{(:[vec(x)]_(B^('))=[[1,-1,2]]^(T)):}
```

Use a software program or a graphing utility to find the transition matrix from

`B`

to

`B^(')`

, find the transition matrix from

`B^(')`

to

`B`

, verify that the two transition matrices are inverses of each other, and find the coordinate matrix

`[vec(x)]_(B)`

, given the coordinate matrix

`[vec(x)]_(B^('))`

. (For each answer, enter an exact number as an integer, fraction, or decimal.) (a) Find the transition matrix from

`B`

to

`B^(')`

.

`P^(-1)=`

(b) Find the transition matrix from

`B^(')`

to

`B`

.

`P=`

(c) Verify that the two transition matrices are inverses of each other.

`PP^(-1)=`

(d) Find the coordinate matrix

`[vec(x)]_(B)`

, given the coordinate matrix

`[vec(x)]_(B^('))`

.

`[vec(x)]_(B)=[,|]`