| ( 1, 1, 1, 1, 1, 1, 1), ( 2^6, 2^5, 2^4, 2^3, 2^2, 2, 1 ), ( 3^6, 3^5, 3^4, 3^3, 3^2, 3, 1 ), ( 4^6, 4^5, 4^4, 4^3, 4^2, 4, 1 ), ( 5^6, 5^5, 5^4, 5^3, 5^2, 5, 1 ), ( 6^6, 6^5, 6^4, 6^3, 6^2, 6, 1 ), ( 7^6, 7^5, 7^4, 7^3, 7^2, 7, 1 ) | = ?

1 Answer
Feb 9, 2018

-24883200

Explanation:

"This is the determinant of a Vandermonde matrix."
"It is known that the determinant is then a product of the"
"differences of the base numbers (that or taken to successive" "powers)."

"So here we have "
(6!)(5!)(4!)(3!)(2!)
"= 24,883,200"

"There is one difference though with the Vandermonde matrix"
"and that is that the lowest powers are normally on the left side"
"of the matrix so the columns are mirrored, this gives an extra"
"minus sign to the result : "

"determinant = -24,883,200"