CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Let [λ] be the greatest integer less than or equal to λ. The set of all values of λ for which the system of linear equations x+y+z=4, 3x+2y+5z=3, 9x+4y+(28+[λ])z=[λ] has a solution is

A
(,9)[8,)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
[9,8)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
R
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
(,9)(9,)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C R
x+y+z=4
3x+2y+5z=3
9x+4y+(28+[λ])z=[λ]

For unique solution Δ0
∣ ∣1113259428+[λ]∣ ∣0
(56+2[λ]20)1(84+3[λ]45)+1(6)0
36+2[λ]393[λ]60
[λ]9
λ(,9)[8,)
and if [λ]=9, Δx=Δy=Δz=0 gives infinite solution.

For λR set of equations have solution.

flag
Suggest Corrections
thumbs-up
34
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
A+B+C=N (N Fixed)
QUANTITATIVE APTITUDE
Watch in App
Join BYJU'S Learning Program
CrossIcon