Let α , β and γ be real numbers. Consider the following system of linear equations x + 2 y + z = 7 x + α z = 11 2 x - 3 y + β z = γ Match each entry in List-I to the correct entries in List-II. List-I List-II P If β = 1 2 7 α - 3 and γ = 28 then the system has 1 a unique solution Q If β = 1 2 7 α - 3 and γ ≠ 28 , then the system has 2 no solution R If

Step-by-step solution

Given, System of equations, x + 2 y + z = 7 x + α z = 11 2 x - 3 y + β z = γ Now finding Δ = 1 2 1 1 0 α 2 - 3 β = 0 ⇒ 3 α - 2 β - 2 α - 3 = 0 ⇒ 7 α - 2 β = 3 ⇒ β = 1 2 7 α - 3 Now finding, Δ 3 = 1 2 7 1 0 11 2 - 3 γ Now equating, Δ 3 = 0 we get, ⇒ 33 - 2 γ - 22 + 7 - 3 = 0 ⇒ γ = 28 And Δ 1 = 7 2 1 11 0 α γ - 3 β ⇒ Δ 1 = 21 α - 2 11 β - α γ - 33 &