engineering recuitment GATE ME 2023-24 Test Series Engineering Mathematics Linear Algebra System of Linear Equations
Suppose α, β, γ ∈ R. Consider the following system of linear equations.
\(x+y+z=\alpha\)
\(x+\beta y+z=\gamma\)
\(x+y+\alpha z=\beta\)
If this system has at least one solution, which of the following statement is TRUE?
1
If α = 1 then β = 1
2
If β = 1 then γ = α
3
If β ≠ 1 then α = 1
4
If γ = 1 then α = 1