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Determine divisibility (Posted on 2014-09-29) Difficulty: 2 of 5
If I tell you that each of the four numbers 1242,1426,2070,and 1564 is divisible by 23(trust me!), could you with no explicit calculation prove that the determinant of the 4x4 matrix
1 2 4 2
1 4 2 6
1 5 6 4
2 0 7 0
is also divisible by 23?

See The Solution Submitted by Ady TZIDON    
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Solution Solution Comment 1 of 1
Multiply the 1st, 2nd and 3rd columns by 1000, 100 and 10 respectively
and add the results to the fourth column. This will not change the
value of the determinant:

1  2  4  1242
1  4  2  1426
1  5  6  1564
2  0  7  2070:

23 is then a common factor of all elements in column 4 and therefore
a factor of the determinant.

(In fact the value of the determinant is 0)




  Posted by Harry on 2014-10-02 19:39:27
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