Given, system of equations x + y + z = 4 3x + 2y + 5z = 3 9x + 4y + (28 + |λ|)z = |λ| Δ=|
1
1
1
3
2
5
9
4
28+|λ|
| = 1(56 + 2|λ| − 20) − 1(84 + 3|λ| − 45) + 1(− 6) = − (|λ| + 9) If ∆ ≠ 0 i.e |λ| + 9 ≠ 0, then system of equation has unique solution. If |λ|+9=0, then Δ1=Δ2=Δ3=0, the system of equation has infinite solution. ⇒ λ ∈ R