Question: Q3. Let a1, 02,..., an be distinct elements of a field K. Consider the Vandermonde matrix 1 1 -(45) 1 an an V :=

Q3. Let a1, 02,..., an be distinct elements of a field K.

Q3. Let a1, 02,..., an be distinct elements of a field K. Consider the Vandermonde matrix 1 1 -(45) 1 an an V := (i) Compute the determinant det (V) when n = 2. (ii) Use induction to show that n-1 a2-1 an- det (V) II (aj - i) 1

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