Linear algebra problem with transpose

[Bohrok]

Homework Statement

Find a formula for (ABx)^T, where x is a vector and A and B are matrices of appropriate sizes.

Homework Equations

(AB)^T = B^TA^T among a few others, probably the most relevant one with transposes here.

The Attempt at a Solution

I'm wondering what this "formula" the problem asks for looks like. I know that (ABx)^T = x^TB^TA^T but I can't really see how much simpler another formula might be.

Any ideas what route to take to find a formula for this, preferable without the use of a lot of summation notation or anything beyond a beginning linear algebra course? We used a lot of summations earlier trying to tackle this problem and it just looked messy; I'm hoping there may be a cleaner way of approaching the problem.

 

[LCKurtz]

Perhaps what the question is getting at is for you to use the formula (AB)^T = B^TA^T which you know works for a product of two conformable matrices and get the formula for three of them from that, being careful about properties of matrix multiplication that you know.

 

[Bohrok]

I got it for three matrices and that was before using all the sums. We didn't really go back to the problem again (she said it was so ugly anyway) so I guess that's it for the problem. :) Thanks