Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide Solution For R.D. Sharma Maths Class 12 Chapter determinants Exercise 5.2 Question 4 Maths Textbook Solution.

Provide Solution For  R.D. Sharma Maths Class 12 Chapter determinants Exercise 5.2 Question 2 sub question 4 Maths Textbook Solution.

Answers (1)

Answer:-\left|\begin{array}{lll} 1 & a & b c \\ 1 & b & c a \\ 1 & c & a b \end{array}\right|=(a-b)(b-c)(c-a)

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

Given:\left|\begin{array}{lll} 1 & a & b c \\ 1 & b & c a \\ 1 & c & a b \end{array}\right|

Solution :\left|\begin{array}{lll} 1 & a & b c \\ 1 & b & c a \\ 1 & c & a b \end{array}\right|

\begin{aligned} &\text { On applying } \mathrm{R}_{1} \rightarrow R_{1}-R_{2} \text { and } \mathrm{R}_{2} \rightarrow R_{2}-R_{3}\\ &=\left|\begin{array}{ccc} 0 & a-b & b c-c a \\ 0 & b-c & c a-a b \\ 1 & c & a b \end{array}\right|\\ &=\left|\begin{array}{ccc} 0 & a-b & -c(a-b) \\ 0 & b-c & -a(b-c) \\ 1 & c & a b \end{array}\right| \end{aligned}

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

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

Hence \left|\begin{array}{lll} 1 & a & b c \\ 1 & b & c a \\ 1 & c & a b \end{array}\right|=(a-b)(b-c)(c-a)

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 OSM controversy deepens as students allege fresh errors, seek grace marks
anam-khan

CBSE to issue revised Class-12 physical marksheets through regional offices
anam-khan

NEET aspirant Aditya Mishra becomes CBSE Science topper after re-evaluation

Latest Question