Show that determinant
2 0 6 0 4
5 3 2 2 7
2 5 7 5 5
2 0 9 2 7
0 0 2 8 9
is divisible by 17
1
Expert's answer
2012-07-27T07:32:46-0400
The determinant will have no changes after adding one column to another, multiplied by some number. So we can 1)multiply first column by 10000 and add to the last one 2)multiply second column by 1000 and add to the last one 3)multiply third column by 100 and add to the last one 4)multiply forth column by 10 and add to the last one
After this elementary column operations last column will be
20604 53227 25755 20927 289 All these numbers are divisible by 17, so as one column is divisible by 17, then the whole determinant is divisible by 17 too.
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