41. Let 1 S = %3D 2 -1 } 4 1 a. Find span(S). b. Is S linearly independent? c. Let -三 T = -1 -1 -3 4 Is span(T) = R³? Is T linearly independent? %3D

Show that t, e^t, and sin(t) are linearly independent.

3

Fit a cubic trend function to the data (-2,6), (-1,8), (0,8), (1,7), (2,6). Let po(t) = 1, p₁ (t) = t and p₂(t) = 1² -2. The orthogonal cubic polynomial is p3(t)=³-t. The vectors for Po. P₁, and p2 are 1 17 p(t) = THI 1 2 (…) NOT~ and -2 respectively.