# | ( 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 ) | = ?

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#### Explanation

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#### Explanation:

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2
Feb 9, 2018

$- 24883200$

#### Explanation:

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

$\text{So here we have }$
(6!)(5!)(4!)(3!)(2!)
$\text{= 24,883,200}$

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

$\text{determinant = -24,883,200}$

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