Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal elements of is 1, then the possible number of such matrices is :  

Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal elements of A^{2} is 1, then the possible number of such matrices is :
 
Option: 1 6
Option: 2 12
Option: 3 1  
Option: 4 4

Answers (1)

best_answer

A=\left(\begin{array}{ll} a & b \\ b & c \end{array}\right), \quad a, b, c \in I

A^{2}=\left(\begin{array}{ll} a & b \\ b & c \end{array}\right)\left(\begin{array}{ll} a & b \\ b & c \end{array}\right)=\left(\begin{array}{cc} a^{2}+b^{2} & b(a+c) \\ b(a+c) & b^{2}+c^{2} \end{array}\right)

Sum of all the diagonal element of 

\\A^{2}=a^{2}+2 b^{2}+c^{2} \\ \text { Given } a^{2}+2 b^{2}+c^{2}=1, a, b, c \in I \\ b=0 \;\;\& \;\;a^{2}+c^{2}=1

\begin{aligned} &\text { Case-1 }: \mathrm{a}=0 \Rightarrow \mathrm{c}=\pm 1 \quad(2 \text { -matrices })\\ &\text { Case-2 }: c=0 \Rightarrow a=\pm 1 \quad \text { (2-matrices) }\\ &\text { Total }=4 \text { matrices } \end{aligned}

Posted by

himanshu.meshram

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main Result 2024 Live: JEE April results at jeemain.nta.ac.in likely today; cutoff, rank predictor, update
anam-khan

JEE Main 2024 session 2 final answer key out at jeemain.nta.ac.in; steps to check probable scores
anam-khan

JEE Main Result 2024 Live: Download session 2 final answer key at jeemain.nta.ac.in; rank predictor, cutoff

Latest Question