Find the general solution of the system whose augmented matrix?

Question

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

a. x1 =

x2 is free

x3 is free

b. x1 =

x2 =

x3 =

c. x1 =

x2 is free

x3 =

d. The system has no solution

Answer 1

[1 3 1 -1] [1 3 1 -1] [1 3 1 -1] [1 3 0 -4]

[2 6 -1 -11] (R1X(-2)+R2-->R2) [0 0 -3 -9] (R2X(-1/3)-->R2) [0 0 1 3] (R2X(-1)+R1-->R1) [0 0 1 3]

In the echelon form of the augmented matrix, the 1st and 3rd columns are pivot columns, so x2 is the free variable. We have

x1+3x2 = -4

x3 = 3,

that is,

x1 = -4 - 3x2

x2 is free

x3 = 3