Question

is there a solution to (a)  x1 + 2x2 + 3x3 = 1 2x1 + 3x2 + 4x3 = 3 x1 + 2x2 + x3 = 3

 

What iss the solution?

Answer 1

Matrix format (Gauss method):

( 1 2 3 | 1 )

( 2 3 4 | 3 )

( 1 2 1 | 3 )

R3-R1:

( 1 2 3 | 1 )

( 2 3 4 | 3 )

( 0 0 -2 | 2 )

R3/-2:

( 1 2 3 | 1 )

( 2 3 4 | 3 )

( 0 0 1 | -1 )

R2-R1:

( 1 2 3 | 1 )

( 1 1 1 | 2 )

( 0 0 1 | -1 )

R1⇔R2:

( 1 1 1 | 2 )

( 1 2 3 | 1 )

( 0 0 1 | -1 )

R2-R1:

( 1 1 1 | 2 )

( 0 1 2 | -1 )

( 0 0 1 | -1 )

R2-R3:

( 1 1 1 | 2 )

( 0 1 1 | 0 )

( 0 0 1 | -1 )

R1-R2:

( 1 0 0 | 2 )

( 0 1 1 | 0 )

( 0 0 1 | -1 )

R2-R3:

( 1 0 0 | 2 )

( 0 1 0 | 1 )

( 0 0 1 | -1 )

x1=2; x2=1; x3=-1. So there is a unique solution.