I have the following question: f1(x),....fn(x) belong to polynomial space with a degree less or equal to n-2 a1,....an belong to the real numbers. what is the determinant of matrix A ?
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Hint: The rows of your matrix are linearly dependent. – darij grinberg Jan 12 '19 at 18:35
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can you please add more? – KIMKES1232 Jan 12 '19 at 19:42
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The polynomials of degree $\leq n-2$ form an $n-1$-dimensional vector space. Hence, their lists of values at $a_1,a_2,\ldots,a_n$ also belong to an at-most-$n-1$-dimensional vector space. Thus, they are linearly dependent. – darij grinberg Jan 12 '19 at 19:48
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thank you! great – KIMKES1232 Jan 12 '19 at 20:28