Question

(1) Calculate the Wronskian of the following vectors and determine if they are pointwise linearly independent or dependent. e 0 0 y(1) ). y (2) y (3) 3e- 3e24 6e2.c 2e34 0 W(y(1), y(2), y(3) Circle One: Independent Dependent

Answer 1

(0) solution: (21 g AN L2e3x Definition: Let ult) and 22 (t) be two -2 recfor function medefine their wronskian as w(472) = y (4) whose column are two vector functions For 3x3, Here 2419 %2 (4) 42 (1) wa 27 o en e j wigs, you, you 27 Зе 3 e-x 2832 6e 6 e za x = 0+0+22321 422 e cable to 362x Be 2 e Lesa ( 3*-3e?) =203"yo so we you, yea, ysg=0 so you, you, ys) are linearly dependent. yel ya, ys are linearly dependent