Use the Gauss Jordan method to solve each system of equations.
5x-4y+2z=4
5x+3y-z=17
15x-5y+3z=25
2007-08-15 05:33:45 · 2 answers · asked by twilliam4055 1 in Science & Mathematics ➔ Mathematics
| 5x-4y+2z=4 #
| 5x+3y-z=17 ##
| 15x-5y+3z=25 ###
###+## - # is 15x+2y=38 so y=19-7.5x @
put @ to ## so z=40-17.5x @@
put @and@@to # so x=??????????????
????????????????????????????????????
okey ,
we can not get x,y,z from the 3
we need more
2007-08-15 07:18:15 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Start with the augmented matrix
5 -4 2 4
5 3 -1 17
15 -5 3 25.
Now (-1)*R1 + R2 --> R2 = 0 7 -3 13, and (-15)*R1 + R3
--> R3 = 0 55 -27 -35. Finally, (-55/7)*R2 + R3 --> R3 =
0 0 -24/7 -960/7. The matrix now is
5 -4 2 4
0 7 -3 13
0 0 -24/7 -960/7.
The third row represents the equation (-24/7)*z = -960/7, so z = 40. Using this value in the second equation, we have
7y - 3*(40) = 13, so y = 19. The first row represents
5x - 4y +2z = 4, so 5x - 4*19 + 2*40 = 4, and x = 0.
Thus, (x, y, z) = (0, 19, 40).
2007-08-17 07:05:24 · answer #2 · answered by Tony 7 · 0⤊ 0⤋