For which of the following ordered pairs μ , δ , the system of linear equations x + 2 y + 3 z = 1 3 x + 4 y + 5 z = μ 4 x + 4 y + 4 z = δ is inconsistent?

Step-by-step solution

D = 3 4 5 1 2 3 4 4 4             R 3 → R 3 - 2 R 1 + 3 R 2 = 3 4 5 1 2 3 0 0 0   = 0 Now, let P 3 ≡ 4 x + 4 y + 4 z - δ = 0 . If the system has solutions it will have infinite solution, so, P 3 ≡ α P 1 + β P 2 Hence, 3 α + β = 4 and 4 α + 2 β = 4 ⇒ α = 2   a n d     β = - 2 So, for infinite solution 2 μ - 2 = δ For system to be inconsistent,   2 μ ≠ δ + 2 So, c