Given a matrix, find position of first non-zero element in each row

• To: mathgroup at smc.vnet.net
• Subject: [mg99492] Given a matrix, find position of first non-zero element in each row
• From: "Nasser Abbasi" <nma at 12000.org>
• Date: Wed, 6 May 2009 05:29:44 -0400 (EDT)
• Reply-to: "Nasser Abbasi" <nma at 12000.org>

```This is a little problem I saw in another forum, and I am trying to also
solve it in Mathematica.

Given a Matrix, I need to find the position of the first occurance of a
value which is not zero in each row.

The position found will be the position in the orginal matrix ofcourse.

So, given this matrix,

A = {
{0, 0, 5},
{50, 0, 100},
{0, 75, 100},
{75, 100, 0},
{0, 75, 100},
{0, 75, 100}
};

The result should be

{{1, 3}, {2, 1}, {3, 2}, {4, 1}, {5, 2}, {6, 2}}

This is how I solved this problem and after a bit of  struggle. I wanted to
see if I could avoid using a Table, and solve it just using Patterns and
Position and Select, but could not so far.

Table[Flatten[{i, Flatten[Position[A[[i,All]], _?(#1 != 0 & ), 1, 1]]}], {i,
1, 6}]

Out[174]= {{1, 3}, {2, 1}, {3, 2}, {4, 1}, {5, 2}, {6, 2}}

I am not happy with the above solution. I am sure there is a better one (the
above also do not work well when one row has all zeros).

Do you see a better and more elegant way to do this?

thanks,
--Nasser

```

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