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## Homework Statement

Find the matrix representations [T]

_{[itex]\alpha[/itex]}and [T]

_{β}of the following linear transformation T on ℝ

^{3}with respect to the standard basis:

[itex]\alpha[/itex] = {

**e**

_{1},

**e**

_{2},

**e**

_{3}}

and β={

**e**

_{3},

**e**

_{2},

**e**}

_{1}T(x,y,z)=(2x-3y+4z, 5x-y+2z, 4x+7y)

Also, find the matrix representation of [T][itex]^{\alpha}_{\beta}[/itex]

## Homework Equations

None

## The Attempt at a Solution

T(

**e**) = (2, 5, 4)

_{1}T(

**e**) = (-3, -1, 7)

_{2}T(

**e**) = (4, 2, 0)

_{3}So, I got [T]

_{[itex]\alpha[/itex]}= (T(

**e**), T(

_{1}**e**), T(

_{2}**e**))

_{3}but for [T]

_{β}, I got [T]

_{β}=(T(

**e**), T(

_{3}**e**), T(

_{2}**e**))

_{1}However, the answers in the back of the book tell me that although my order for [T]

_{β}is correct, the vectors themselves are inverted.

ie: T(

**e**) = (4, 5, 2)

_{1}Why is this? And I'm not sure how to start the second half of the question...