Question: Consider a set of polynomials {p1(t), . . . , pm(t)} in Pn with pi(t) = a i 0 + a i 1 t +

Consider a set of polynomials {p1(t), . . . , pm(t)} in Pn with pi(t) = a i 0 + a i 1 t + + a i n t n for i = 1, . . . , n. Show that dim Span(p1(t), . . . , pm(t)) is the same as the rank of the following matrix ? ? ? a 1 0 a 2 0 . . . an 0 . . . . . . a 1 n a 2 n . . . an n ? ? ?

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Problom 2. Consider a. set of polynomials {p1(t), . .. ,pm(t)} in P.\" with 101-05) = of) + {fit + - - - + oat\" for 15 = 1, . . . ,n. Show that dim Span(p1(t), . . . ,pm(t)) is the same as the rank of the following matrix (1(1) :13 a3 ax}1L 531 a

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