Thread: Prove that the det of a Matrix is divisible by 19 given...

So, I'm given this question that I am REALLY stuck on, I honestly have no idea where to begin, it's got me absolutely stumped and none of the information I have on hand helps me out (Unless I'm overlooking something simple). Anyway, the question is:

The five numbers 21,375 38,798 34,162 40,223 and 79,154 are all divisible by 19. Prove that the determinant of the matrix:



is also divisible by 19

Any help would be appreciated

Originally Posted by AlmightyMidget

So, I'm given this question that I am REALLY stuck on, I honestly have no idea where to begin, it's got me absolutely stumped and none of the information I have on hand helps me out (Unless I'm overlooking something simple). Anyway, the question is:

The five numbers 21,375 38,798 34,162 40,223 and 79,154 are all divisible by 19. Prove that the determinant of the matrix:



is also divisible by 19

Any help would be appreciated

do this column operation and you'll be done (here is the j-th column):

How did tou figure it out? Is there a general way to do it

Originally Posted by pankaj

How did tou figure it out? Is there a general way to do it

i think if you do what i suggested in my previous post, you'll see how i figured it out.

Thanks very much NonCommAlg! I did what you suggested during my break today, and I almost kicked myself, it seems so simple, thanks!

Originally Posted by AlmightyMidget

So, I'm given this question that I am REALLY stuck on, I honestly have no idea where to begin, it's got me absolutely stumped and none of the information I have on hand helps me out (Unless I'm overlooking something simple). Anyway, the question is:

The five numbers 21,375 38,798 34,162 40,223 and 79,154 are all divisible by 19. Prove that the determinant of the matrix:



is also divisible by 19

Any help would be appreciated

Wait the 5 numbers are ordered pairs: 21,375 38,798 34,162 40,223 and 79,154?