Question 18984
 L(x1,x2,x3) = (x3, x1+2x2-5x3, x1-x2) ? 
 (FORGET yur wrong idea.)

 It is linear, just try to check the linearity directly:
 
 L(a(x1,x2,x3)+b(y1,y2,y3))  =  a L(x1,x2,x3) + b L(y1,y2,y3)
 

 Kenny