2. Consider the following system of three linear equations in three unknowns: x₁ + x₂ + ax₂ = 1 x₂ + ax₂ + x₂ = 3 [ax₂ + x^₂ + x₂ = 2a where a € R. (a) Find condition on a such that the system has a unique solution. (b) Find condition on a such that the system has no solution. (c) Find condition on a such that the system has many solutions.

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