#### 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`

C_{2} → C_{2} – C_{1} ; C_{3} → C_{3} – C_{1}

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

expansion along R_{1}

-(k-3)-3≠0

-k+3-3 ≠ 0

k ≠ 0

Is there an error in this question or solution?

Solution 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? Concept: Elementary Transformations.