CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

If α and β are the roots of the equation 1+x+x2=0, then the matrix product
[1βαα][αβ1β] is equal to

A
[1112]
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
[1112]
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
[1112]
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
[1112]
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A [1112]
α,β are roots of x2+x+1=0
α=ω,β=ω2

Putting these value in equation given we get,
ω+ω2=1ω2+ω4=1

As we know that , α+β=1
and αβ=1=ω3

[1βαα] [αβ1β]=[α+ββ+β2α2+ααβ+αβ]=[ω+ω2ω4+ω2ω2+ω2ω3]= [1112]

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Multiplication of Matrices
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon