Find the general solution for the linear system represented by the augmented matrix B, below.

Question

Find the general solution for the linear system represented by the augmented matrix B, below.

1 -4  0  0  4 0  2

0  0  1  0  5 0 -2

0  0  0  1  2 0  0

0  0  0  0  0 1  3

⎡

=  

 

  +  

 

 

  + 

 

 

 

Answer 1

do row operations until you get 1's in the diagonal and 0's everywhere else. in the first 6 columns. then the solution will be in the last, 7th column

but that's impossible as it's not a square matrix

so, you get an infinite number of solutions

a -4b +4y = 2

c -5y = -2

x + 2y = 0

z = 3

6 variables, only 4 equations, no unique solution except for z=3