Suppose f1(t).........fk(t) are vector-valued functions from R to Rn. (a) Prove that if f1(t0),. . . fk(t0)
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(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
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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to 21 -1 fi(r) and fa()-
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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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