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

The value of determinant ∣ ∣abb+cabcc+abcaa+bc∣ ∣ is

A
a3+b3+c3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
3abc
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
a3+b3+c33abc
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
a3+b3+c3+3abc
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C a3+b3+c33abc
=∣ ∣abb+cabcc+abcaa+bc∣ ∣

Applying R1R1+R2+R3, we get
=(a+b+c)∣ ∣021bcc+abcaa+bc∣ ∣

Expanding along R1, we get
=(a+b+c)[2c(bc)+2b(ca)+(bc)(a+b)(ca)(c+a)]
=(a+b+c)(a2+b2+c2abbcac)
=a3+b3+c33abc

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