(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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]

2. Relevant equations

None

3. 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...

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Linear Algebra question regarding Matrices of Linear Transformations

**Physics Forums | Science Articles, Homework Help, Discussion**