Replace a Single Element in a Matrix

Question

Given:

l:4 cut til 16

0  1  2  3
4  5  6  7
8  9  10 11
12 13 14 15

Replace the number 11 with the number 40.

Expected result:

0  1  2  3
4  5  6  7
8  9  10 40
12 13 14 15

Solution

.[l;(2;3);:;40]

Explanation

. is amend applied with a path of indexes rather than a single one — .[x;(i;j);:;y] drills down into x at row i, column j, and sets that one value to y, leaving everything else in the matrix untouched.

Here (2;3) addresses row 2 (8 9 10 11), position 3 within that row (the value 11), and replaces it with 40. This is the natural extension of @[x;i;:;y] to nested structures: @ amends a single level of a list, while . follows a path through multiple levels — exactly what's needed to reach into one cell of a matrix without rebuilding the whole thing.