1.2.18 Determinant Calculation

Condition: Dove that if \ (k_ {1}, k_ {2}, \ ldots, k_ {n-1}- \) various natural numbers, \ (a_ {1}, a_ {2}, \ ldots, a_ {n}- \) Various positive numbers, then the determinant \ ( \ Left | \ Begin {Array} {cccc} 1 & 1 & \ ldots & 1 \\ a_ {1}^{k_ {1} & a_ {2} {K_ {1}} & \ ldots & a_ {n}^{k_ {1}} \\ \ ldots & \ ldots & \ ldots & \ cdots \\ a_ {1}^{n-1} & a_ {2}^{n-1}} & \ ldots & a_ {n}^{k_ {n-1}} \ end {Array} \ Right |.