Question

For what values of k, the system of linear equations

x + y + z = 2
2x + y – z = 3
3x + 2y + kz = 4

has a unique solution?

 

Answer 1

for unique solution |A|≠ 0

`|(1,1,1),(2,1,-1),(3,2,k)|!=0`

C₂ → C₂ – C₁ ; C₃ → C₃ – C₁

`|(1,0,0),(2,-1,-3),(3,-1,k-3)|!=0`

expansion along R₁

-(k-3)-3≠0

-k+3-3 ≠ 0

k ≠ 0