Question

apply gauss- Jordan method to solve the following system of equations x+y+z=9;2x-3y+4z=13;3x+4y+5z=90.​

Answer 1

Answer:

x+y+z=9→(1)

2x+y-z=0→(2)

2x+5y+7z=52→(3)

Select the equations (1) and (2), and eliminate the variable x.

x+y+z=9 ×2→ 2x + 2y + 2z = 18

−

2x+y-z=0 ×1→ 2x + y - z = 0

y + 3z = 18 →(4)

Select the equations (1) and (3), and eliminate the variable x.

x+y+z=9 ×2→ 2x + 2y + 2z = 18

−

2x+5y+7z=52 ×1→ 2x + 5y + 7z = 52

- 3y - 5z = -34 →(5)

Select the equations (4) and (5), and eliminate the variable y.

y+3z=18 ×3→ 3y + 9z = 54

+

-3y-5z=-34 ×1→ - 3y - 5z = -34

4z = 20 →(6)