wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If matrix A=⎡⎢⎣abcbcacab⎤⎥⎦ where a, b, c are real positive numbers, abc = 1 and ATA=I, then the value of a3+b3+c3 is ___.

A
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
4
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D 4
Given, A=abcbcacab,abc=1 and AT A=INow,AT A=1abcbcacababcbcacab=100010001a2+b2+c2ab+bc+caab+bc+caab+bc+caa2+b2+c2ab+bc+caab+bc+caab+bc+caa2+b2+c2=100010001a2+b2+c2=1 and ab+bc+ca=0.....(ii)we know a3+b3+c33abc=(a+b+c)(a2+b2+c2abbcca)a3+b3+c3=(a+b+c)(10)+3[From Eqs.(i)and(iii)]a3+b3+c3=(a+b+c)+3.......(iii)Now,(a+b+c)2=a2+b2+c2+2(ab+bc+ca)=1......(iv)From,Eq.(iii),a3+b3+c3=1+3a3+b3+c3=4.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Adaptive Q1
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon