wiz-icon
MyQuestionIcon
MyQuestionIcon
23
You visited us 23 times! Enjoying our articles? Unlock Full Access!
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?

A
(4,6)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
(3,4)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
(1,0)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
(4,3)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D (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∣ ∣=2(2μδ2) (i)

Dy=∣ ∣1133μ54δ4∣ ∣=4(δ+2μ2) (ii)

Dz=∣ ∣12134μ44δ∣ ∣=2(δ2μ+2) (iii)
For inconsistent system, we get from (i),(ii) and (iii)
2μδ+2
From the provided options, the system will be inconsistent for μ=4,δ=3.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon