Consider a basis / 1, ..., f n of Pn- \ . Let a \,..., an be distinct real numbers
Chapter 4, Problem 69(choose chapter or problem)
Consider a basis / 1, ..., f n of Pn- \ . Let a \,..., an be distinct real numbers. Consider the n x n matrix M whose 1 yth entry is /,(/). Show that the matrix M is invertible. [Hint: If the vectoris in the kernel of M, then the polynomial / = C\ f\ H---------------- + cnfn in pn- 1 vanishes at a\..an\ therefore, / = 0.]
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