Question

Find the general solution of the system whose augmented matrix is given below. 1 -2 0 -1 0-6 0 10 0 -8 9 000 1 83 0 0 0 0 0 X2 is free {X3 is free X3 is free *3 X4 is free Xs is free X- is free Click to select and enter your answer(s) and then click Check Answer.

Answer 1

Cliven the augmented matopx P4 -2 0 To 1 0 TO 0 0 Lo o o -1 0 -67 0 -8 g I 8 3 o o ol "The augmented manex is Pn Pts dow echelon. form to leading is comesponds to variables 1, 3, 4 X . . : Xa and X5 are free variables we have the equations *, - 2x2 - X4 2-6 x) - 8x - 3 x +8 X = 3 X3 and xg are free variables, ie. X₃, Xs ER, we have from equation X4 = 3 - 8X5 x = 3 + 8 X- * E-6+2X2 + x4 = -64 213-8*5) +($ and X = -6 + 2X2 + --6+2(978X5] + 3-8X5 - - 6+ 18 + 16X5+3 -8X3

x = 15+ 8X5 X = 15+885 X) = 3+8xc X4 = 3-885 Xz is free variable Xs is free ranable This is the required answed