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Question

For which of the following ordered pairs (μ,δ), the system of linear equations
x+2y+3z=1
3x+4y+5z=μ
4x+4y+4z=δ
is inconsistent?
  1. (3,4)
  2. (1,0)
  3. (4,3)
  4. (4,6)


Solution

The correct option is C (4,3)
D=∣ ∣123345444∣ ∣

R3R3+2R12R2
D=∣ ∣123345000∣ ∣=0

For inconsistent system, one of Dx,Dy,Dz should not be equal to 0
Dx=∣ ∣123μ45δ44∣ ∣

Dy=∣ ∣1133μ54δ4∣ ∣

Dz=∣ ∣12134μ44δ∣ ∣
For inconsistent system, 2μδ+2
The system will be inconsistent for μ=4,δ=3.

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