Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Please Solve R. D. Sharma class 12 Chapter determinants Exercise 5.2 Question 6 Maths textbook Solution.

Please Solve R. D. Sharma class 12 Chapter determinants Exercise 5.2 Question 2 sub question 6 Maths textbook Solution.

Answers (1)

Answer:\left|\begin{array}{lll} a & b & c \\ c & a & b \\ b & c & a \end{array}\right|=(a+b+c)\left(a^{2}+b^{2}+c^{2}-a b-b c-c a\right)

Hint :We will try to make some elements of the determinant into zero

Given :\left|\begin{array}{lll} a & b & c \\ c & a & b \\ b & c & a \end{array}\right|

Solution: \left|\begin{array}{lll} a & b & c \\ c & a & b \\ b & c & a \end{array}\right|

\begin{aligned} &\text { On applying } \mathrm{R}_{1} \rightarrow R_{1}+R_{2}+R_{3} \\ &=\left|\begin{array}{ccc} a+b+c & a+b+c & a+b+c \\ c & a & b \\ b & c & a \end{array}\right| \end{aligned}

\begin{aligned} &\text { On taking common }(a+b+c) \text { from } \mathrm{R}_{1}\\ &=(a+b+c)\left|\begin{array}{lll} 1 & 1 & 1 \\ c & a & b \\ b & c & a \end{array}\right|\\ &\text { On applying } \mathrm{C}_{1} \rightarrow C_{1}-C_{2} \text { and } \mathrm{C}_{2} \rightarrow C_{2}-C_{3}\\ &=(a+b+c)\left|\begin{array}{ccc} 0 & 0 & 1 \\ c-a & a-b & b \\ b-c & c-a & a \end{array}\right| \end{aligned}

\begin{aligned} &\text { On expanding w.r.t } \mathrm{R}_{1}\\ &=(a+b+c)\left[0\left|\begin{array}{ll} a-b & b \\ c-a & a \end{array}\right|-0\left|\begin{array}{cc} b-a & b \\ 0 & a \end{array}\right|+1\left|\begin{array}{cc} c-a & a-b \\ b-c & c-a \end{array}\right|\right.\\ &=(a+b+c)[0-0+1\{(c-a)(c-a)-(b-c)(a-b)\}]\\ &=(a+b+c)\left\{\left(c^{2}-a c-a c+a^{2}\right)-\left(b a-b^{2}+a c-b c\right)\right\}\\ &=(a+b+c)\left(a^{2}+b^{2}+c^{2}-a b-b c-c a\right) \end{aligned}

Hence \left|\begin{array}{lll} a & b & c \\ c & a & b \\ b & c & a \end{array}\right|=(a+b+c)\left(a^{2}+b^{2}+c^{2}-a b-b c-c a\right)

Posted by

infoexpert21

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 12 English Paper Analysis: Questions easy, ‘student-friendly’; can 'score above 90%'
anam-khan

CBSE Class 12 Board Exam 2026 LIVE: 12th English paper easy, 'competency-based questions' for literature
anam-khan

QR code in CBSE Class 12 maths paper redirects to 'rickroll' prank video; board says exam integrity intact

Latest Question