How do you solve the below equation using reduced row-echelon form?

2x+3y-4z=9
x+y+z=3
2x+y-3z=2

1 Answer
Ananda Dasgupta
Feb 25, 2018

x = -7/11,y = 39/11, z = 1/11

Explanation:

Start with the augmented matrix (A|b)

((2,3,-4,|,9),(1,1,1,|,3),(2,1,-3,|,2))

We carry out row reductions to transform this to the reduced row-echelon form. We first swap rows 1 and 2 (this is not necessary - but will cut down some of the computation)

((1,1,1,|,3),(2,3,-4,|,9),(2,1,-3,|,2))

R_2 -> R_2-2R_1, R_3->R_3-2R_1
((1,1,1,|,3),(0,1,-6,|,3),(0,-1,-5,|,-4))

R_1->R_1-R_2, R_3->R_3+R_2
((1,0,7,|,0),(0,1,-6,|,3),(0,0,-11,|,-1))

R_3 -> R_3/{-11}
((1,0,7,|,0),(0,1,-6,|,3),(0,0,1,|,1/11))

R_1 -> R_1-7R_3, R_2 -> R_2+6R_3
((1,0,0,|,-7/11),(0,1,0,|,39/11),(0,0,1,|,1/11))

This gives
x = -7/11,y = 39/11, z = 1/11

Related questions
See all questions in Reduced Row Echelon Form
Impact of this question
3478 views around the world
You can reuse this answer
Creative Commons License