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 rd sharma maths class 12 chapter adjoint and inverse of a matrix exercise multiple choice question question 15

Provide solution for rd sharma maths class 12 chapter adjoint and inverse of a matrix exercise multiple choice question question 15

Answers (1)

 option (c) 16A

Given: A=\begin{bmatrix} 2 &0 &0 \\ 0 & 2& 0\\ 0&0 &2 \end{bmatrix}

Hint:  you must know the multiplication concept of matrices

Solution:

 
\begin{aligned} &\mathrm{A}^{2}=\mathrm{A} \cdot \mathrm{A}\left[\begin{array}{lll} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{array}\right]\left[\begin{array}{lll} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{array}\right] \\ &=\left[\begin{array}{lll} 4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4 \end{array}\right] \\ &A^{5}= A^{2} \cdot A^{2} \cdot A \\ &A^{5}=\left[\begin{array}{lll} 4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4 \end{array}\right]\left[\begin{array}{lll} 4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4 \end{array}\right] \text { A } \end{aligned}

\begin{aligned} &=\left[\begin{array}{ccc} 16 & 0 & 0 \\ 0 & 16 & 0 \\ 0 & 0 & 16 \end{array}\right] \mathrm{A} \\ &=16\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right] \text { A } \\ &= 16 \mathrm{I} \mathrm{A} \\ &\Rightarrow \mathrm{A}^{5}=16 \mathrm{~A} \end{aligned}

 

Hence, option (c) is correct

Posted by

Info Expert 29

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