# Find number by solving the pattern

I need to solve the pattern in given format

98     |    54     |   78
7641   |    3120   |   5402
714    |    494    |   726


43     |    56     |   02
4910   |    0298   |   7614
391    |    005    |   596


35     |    78     |   38
9081   |    4391   |   4602
234    |    823    |   ???


I have to find the last number with question mark.

Edit

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• If you did not make this problem up, please provide a citation for the source. – Jeff Zeitlin Jan 29 '18 at 15:49
• As in a school quiz? – Herb Wolfe Jan 29 '18 at 17:17
• Is this strictly math? I ask because I don't want to go down a rabbit hole of discovering patterns within the numbers themselves only to find out later that the answer required knowledge of something completely different, like patterns in the periodic table or sports stats. – doggify Jan 31 '18 at 19:53
• Mind if I ask what kind of class this was given in? I need to know how to approach the problem. How I've been doing it so far hasn't lead anywhere. – doggify Feb 1 '18 at 7:59
• If it is unimportant than both middle values for 78 are shifted by 1. Maybe that's something important... :/ 5402 - 1 on each position is 4391. – Morfium Feb 5 '18 at 10:09

The determinant of the third matrix is (196389516 - 554633$x$) (here I replaced ??? by $x$ for readability reasons).