||'''Book'''|| Advanced Engineering Mathematics ||
 ||'''Author'''|| Erwin Kreyszig ||
 ||'''Edition'''|| 8th Edition ||

/* code_begins */

{{{
x=var('x')
w=var('w')
W=det(matrix([[exp(-x)*cos(w*x),exp(-x)*sin(w*x)],[exp(-x)*(-w*sin(w*x)-cos(w*x)),exp(-x)*(w*cos(w*x)-sin(w*x))]]))        
show(W.simplify_rational())
#W!=0, so the basis functions are linearly independent}}}

/* code_ends */

 * '''Solution by''': 
   * namdev, teaching, RGIT
   * dilip, teaching, rgit