What is the value of m for QRPT to be defined?

[doxa1]

1. Suppose P is a 5x4 matrix, Q is an nxm matrix and R is a 3x2 matrix. If (QR)T P is defined then ...

a) n=4, m=3 or
b) n=4, m=2

I have no idea what to do. This is basic stuff... I am doing a correspondence course (no lecturers to help), so I am stuck at this and some of my other questions. Where do I start in solving this? I really want to grasp linear algebra and not just get an answer.

I know that a 5x4 matrix has 5 rows and 4 columns and that is = P. What do they mean by (QR)T?

I think that someone who understands this will easily see what they are referring to and unfortunately I am not there at the moment.

 

[Coto]

Hey doxa1, I'm guessing they are asking about the transpose. That is, it should be:

(QR)^{T}P

You can find out what transpose is here: http://en.wikipedia.org/wiki/Transpose

In order to solve the problem you need to understand matrix multiplication: http://en.wikipedia.org/wiki/Matrix_multiplication

Hope this helps.

 

[doxa1]

Hey, thanks for the links...will check it out.

 

[HallsofIvy]

In order to multiply AB where A is an m by n matrix and B is a u by v matrix, ("m by n" meaning "m rows, n columns") we must have n= u and the result will be an m by v matrix.

Since Q is m by n and R is 3 by 2, in order to multiply QR we must have n= 3 and then QR is m by 2 which means its transpose is 2 by m. Now what must m be in order to multiply that by P, a 5 by 4 matrix?