chomp $_;
 my $line = $_;
 my @array =
  map {
   s/^\s+//;  # strip leading spaces
   s/\s+$//;  # strip tailing spaces
   $_         # return the modified string
  }
 split '\s+', $line;
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You don't need anything this complicated.    Just do this:

 my @array = split;
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 print @array."\n"; # prints number of elements instead of whole array
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The concatenation operator (.) forces scalar context on its operands and an array in scalar context returns the number of elements in the array.    You need to use list context instead:

 print @array, "\n";
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 $hash->{$line_num}=@array; # does not works because of previous issue
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Again you are forcing scalar context on the array which evaluates to the number of elements in the array.    If you want to store the contents of the array then you have to either store a reference of the array:

 $hash->{ $line_num } = \@array;
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or copy the array to an anonymous array.

 $hash->{ $line_num } = [ @array ];
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In other words your while loop could be written more simply as:

while ( <FH> ) {
    $hash->{ $. } = [ split ];
}
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But if you are using the line number as hash keys then you should probably be using an array instead of a hash.

my @data;
while ( <FH> ) {
    push @data, [ split ];
}
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Or:

my @data = map [ split ], <FH>;
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Recycling my answer from here

To build a hashe of arrays , you need to store, arrayrefs in the hash, like this

#!/usr/bin/perl --
use strict;
use warnings;

my %foo;
my @bar;
$foo{bar}=\@bar;
$foo{BAR}=\@bar;
for ( 1 .. 2){
    my @arr = "ab$_" .. "ab4";
    $foo{$_} = \@arr;
}

use Data::Dumper;
print Dumper( \%foo );
__END__
$VAR1 = {
          '1' => [
                   'ab1',
                   'ab2',
                   'ab3',
                   'ab4'
                 ],
          'bar' => [],
          'BAR' => $VAR1->{'bar'},
          '2' => [
                   'ab2',
                   'ab3',
                   'ab4'
                 ]
        };
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See the \ operator takes a reference, to an array (\@array), to a hash (\%hash), to a scalar (\$scalar)

See Tutorials: References quick reference