Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Please solve RD Sharma class 12 chapter Algebra of matrices exercise 4.3 question 39 maths textbook solution

Please solve RD Sharma class 12 chapter Algebra of matrices exercise 4.3 question 39 maths textbook solution

Answers (1)

Answer: x=1 / 5

Hint: I_{3} is an identity matrix of size

3, I_{3}=\left[\begin{array}{rrr}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]

Given:\left[\begin{array}{ccc}2 & 0 & 7 \\ 0 & 1 & 0 \\ 1 & -2 & 1\end{array}\right]\left[\begin{array}{ccc}-x & 14 x & 7 x \\ 0 & 1 & 0 \\ x & -4 x & -2 x\end{array}\right] equal to an identity matrix

So, according to given criteria

\left[\begin{array}{ccc}2 & 0 & 7 \\ 0 & 1 & 0 \\ 1 & -2 & 1\end{array}\right]\left[\begin{array}{ccc}-x & 14 x & 7 x \\ 0 & 1 & 0 \\ x & -4 x & -2 x\end{array}\right]=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]

Now, we will multiply the two matrices in LHS we get

=\left[\begin{array}{ccc}-2 x+0+7 x & 2(14 x)+0+7(-4 x) & 2(7 x)+0+7(-2 x) \\ 0+0+0 & 0+1(1)+0 & 0+0+0 \\ 1(-x)+0+1(x) & 1(14 x)+(-2)(1)+1(-4 x) & 1(7 x)+0+1(-2 x)\end{array}\right] \\\\\\ =\left[\begin{array}{ccc}5 x & 28 x-28 x & 14 x-14 x \\ 0 & 0+1+0 & 0\end{array}\right]\\\\

=\left[\begin{array}{ccc}5 x & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 10 x-2 & 5 x\end{array}\right]

LHS=RHS (given)

\left[\begin{array}{ccc}5 x & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 10 x-2 & 5 x\end{array}\right]=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]

And to satisfy the above condition of equality, the corresponding entries of the matrices should be equal.

So, we get

5x=1

x=1/5

So, the value of x is 1/5

Posted by

infoexpert22

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

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14
anam-khan

CBSE Board Exams 2025: Online portal for availing exemptions by CWSN students opens
anam-khan

Board Exams: States agree to equivalence; no question paper ‘jumbling’ from next year, says PARAKH CEO

Latest Question