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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?
Solution
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
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