Suppose f1(t).........fk(t) are vector-valued functions from R to Rn.
(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.

Transcribed Image Text:

to 21 -1 fi(r) and fa()-