I am trying to follow an example problem so I can solve the real problem. (Same set up different numbers.) I can follow along until the part in the red box. they say "given x2 = 1" Why is that given? They then solve x1 for -5. I don't know how they got that number either. How do we get these answers?

5 -25 Given A = 4 20 , find one nontrivial solution of Ax = 0 by inspection. [Hint: Think of the equation Ax =0 written as a vector equation.] - 35 - 5 - 25 4 20 0 -7 -35 O -25 X1 4 + X2 20 0 - 35 O What is goin on here? Why does X2= 1? O - 25 0 , determine the value of x, using this relationship, given x2 = 1. X2 20 =5X2 For the vector equation (x, + 5x2)[ - 35 -5 - 5 X, = -5 How did we get -5 for x1? . 5 X1 4 + 5X2 4 = (X1 +5X2) 4 So a nontrivial solution is x = I understand, to this point