Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Need solution for RD Sharma maths class 12 chapter Algebra of matrices exercise 4.3 question 29 math

Need solution for RD Sharma maths class 12 chapter Algebra of matrices exercise 4.3 question 29 math

Answers (1)

Answer: Hence, proved A^{2}-5 A+7 I_{2}=0

Hint: I_2 is the identity matrix of size 2.         

I_{2}=\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right] \\

Given: A=\left[\begin{array}{cc} 3 & 1 \\ -1 & 2 \end{array}\right]

Prove:A^{2}-5 A+7 I_{2}=0

Consider:
A^{2}-5 A+7 I_{2} \\\\ =\left[\begin{array}{cc} 3 & 1 \\ -1 & 2 \end{array}\right]\left[\begin{array}{cc} 3 & 1 \\ -1 & 2 \end{array}\right]-5\left[\begin{array}{cc} 3 & 1 \\ -1 & 2 \end{array}\right]+7\left[\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}\right] \\\\\

=\left[\begin{array}{cc} 8-15+7 & 5-5+0 \\ -5+5+0 \quad 3-10+7 \end{array}\right] \\\\\\ =\left[\begin{array}{ll} 0 & 0 \\ 0 & 0 \end{array}\right]

Hence, A^{2}-5 A+7 I_{2}=0

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

CBSE Class 12 supplementary practical exams from July 29; check exam guidelines, rules
anam-khan

CBSE Class 12 supplementary admit card out; exam on July 28 for over 2.5 lakh
anam-khan

CBSE Class 12 supplementary exams 2026 datesheet out; test on July 28

Latest Question