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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? - Mathematics

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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?

 

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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

Concept: Elementary Transformations
  Is there an error in this question or solution?
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