Matrices and Determinants Part 2

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