Find the general solution of the system whose augmented matrix is given below

Question

Chose one:

1.x1 =

x2 =

x3 is free

2.x1 =

x2 =

x3 =

3.x1=

x2 is free

x3 is free

4.The system has no solution

Answer 1

[0 1 -4 3] [1 -4 10 -8] [1 0 -6 4]

[1 -4 10 -8] (R1<--->R2) [0 1 -4 3] (R2X4+R1--->R1) [0 1 -4 3]

In the echelon form of the augmented matrix, the 1st and 2nd columns are pivot columns, so x3 is the free variable. Hence, we have

x1 - 6x3 = 4

x2 - 4x3 = 3,

that is,

x1 = 4+6x3

x2 = 3+4x3

x3 is free