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

Board Exam Time Table 2025 Live: UP Board exams from February 24; CBSE, BSEB date sheet soon
anam-khan

CBSE Date Sheet 2025 Live: Class 10, 12 board exam dates soon; syllabus, sample papers
anam-khan

Extra time in CBSE exams for students with type 1 diabetes: Kerala SHRC seeks report on plea

Latest Question