Suppose f1(t).........fk(t) are vector-valued functions from R to Rn. (a) Prove that if f1(t0),. . . fk(t0)
Question:
(a) Prove that if f1(t0),. . . fk(t0) afe linearly independent vectors in Rn at one fixed to, then f1 (t),. . . fk(t) are linearly independent functions.
(b) Show that
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are linearly independent functions, even though at each fixed to, the vectors f1(t0). f2(t0) are linearly dependent. Therefore, the converse to the result in part (a) is not valid.
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a Suppose c 1 f 1 t c n f n t 0 for all t Then c 1 f 1 t 0 c n f n t 0 0 and hence by line...View the full answer
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