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 41 sub question 1 Maths textbook Solution.

Please Solve R.D. Sharma class 12 Chapter determinants Exercise  5. 2 Question 41 sub question 1 Maths textbook Solution.

Answers (1)

Answer: a^{3}+3 a^{2}

Hint Use determinant formula

Given:\left|\begin{array}{ccc} 1+a & 1 & 1 \\ 1 & 1+a & 1 \\ 1 & 1 & 1+a \end{array}\right|=a^{3}+3 a^{2}

Solution:

\begin{aligned} &\text { L.H.S }\left|\begin{array}{ccc} 1+a & 1 & 1 \\ 1 & 1+a & 1 \\ 1 & 1 & 1+a \end{array}\right| \\ &\quad \text { Apply } \mathrm{C}_{1} \rightarrow C_{1}+C_{2}+C_{3} \\ &=\left|\begin{array}{ccc} a+3 & 1 & 1 \\ a+3 & 1+a & 1 \\ a+3 & 1 & 1+a \end{array}\right| \end{aligned}

\begin{aligned} &(a+3) \text { common from } \mathrm{C}_{1}\left[C_{1} \rightarrow \frac{C_{1}}{a+3}\right] \\ &=(a+3)\left|\begin{array}{ccc} 1 & 1 & 1 \\ 1 & 1+a & 1 \\ 1 & 1 & 1+a \end{array}\right| \end{aligned}

\begin{aligned} &\text { Now } \mathrm{C}_{3} \rightarrow C_{3}-C_{1} \\ &=(a+3)\left|\begin{array}{ccc} 1 & 1 & 0 \\ 1 & 1+a & 0 \\ 1 & 1 & a \end{array}\right| \end{aligned}

Expanding w.r.t C_{3}

\begin{aligned} &=(a+3)\left\{a \mid \begin{array}{cc} 1 & 1 \\ 1 & 1+a \end{array}\right\} \\ &=(a+3)\{a(1+a-1)\} \\ &=(a+3) a^{2} \\ &=a^{3}+3 a^{2} \\ &=R H . S \end{aligned}

 

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

Ace CBSE board exam time management, pattern with previous years’ question papers
anam-khan

No toppers list this year? Highest marks obtained in CBSE Class 12 board exam
anam-khan

CBSE announces STEM education as annual training theme for 2025

Latest Question