F# Programming

The transpose of a matrix M is the matrix obtained by reflecting M about its diagonal. For example, the transpose of

/ 1 2 3 \

\ 4 5 6 /

is

/ 1 4 \

| 2 5 |

\ 3 6 /

An m-by-n matrix can be represented in F# as a list of m rows, each of which is a list of length n. For example, the first matrix above is represented as the list

[[1;2;3];[4;5;6]]

Write an efficient F# function to compute the transpose of an m-by-n matrix:

> transpose [[1;2;3];[4;5;6]];;

val it : int list list = [[1; 4]; [2; 5]; [3; 6]]

Assume that all the rows in the matrix have the same length.

Hints: transpose [] should give an error message --- Use failwith

transpose [[]] is [] // Input argument is a list with one element, the empty list.