Given that the numbers 21375 38798 34162 40223 and 79154 are

Given that the numbers 21375, 38798, 34162, 40223 and 79154 are all multiples of 19 prove that the determinant of the following matrix is also divisible by 19.

Solution

For this w e will do

The point being that 2(10000)+ 1(1000)+ 3(100)+ 7(10)+ 5= 21375, 3(10000)+ 8(1000) +7(100)+ 9(10)+ 8= 38798, etc. That particular linear combination of the numbers on any one row is divisible by the same number.

which it will give   19 * 2042=38798    it is true