Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Questions  >>  CBSE XII  >>  Math  >>  Matrices
Answer
Comment
Share
Q)

Construct a $2 \times 2$ matrix, $A=[a_{ij}],$whose elements are given by: $a_{ij}=\frac{(i+j)^2}{2}\qquad$

$\begin{array}{1 1} \begin{bmatrix}1 & \frac{9}{2}\\\frac{9}{2} & 8\end{bmatrix} \\\begin{bmatrix}2 & \frac{9}{2}\\\frac{9}{2} & 8\end{bmatrix} \\ \begin{bmatrix}2 & \frac{9}{3}\\\frac{9}{2} & 8\end{bmatrix} \\ \begin{bmatrix}2 & \frac{9}{2}\\\frac{9}{2} & -8\end{bmatrix} \end{array} $

1 Answer

Comment
A)
Toolbox:
  • In general $a_{2\times 2}$ matrix is given by\[\begin{bmatrix}a_{11} & a_{12}\\a_{21} & a_{22}\end{bmatrix}\]
  • Elements are given by $a_{ij}=\frac{(i+j)^2}{2}$, where (i, j) can be either (1,1), (1,2), (2,2) or (2,1)
Given, $a_{ij}=\frac{(i+j)^2}{2}, \Rightarrow$
$a_{11}=\frac{(1+1)^2}{2}=\frac{2^2}{2}=\frac{4}{2}=2.$
$a_{12}=\frac{(1+2)^2}{2}=\frac{3^2}{2}=\frac{9}{2}.$
$a_{21}=\frac{(2+1)^2}{2}=\frac{3^2}{2}=\frac{9}{2}.$
$a_{12}=\frac{(2+2)^2}{2}=\frac{4^2}{2}=\frac{16}{2}=8.$
Hence the required matrix is given by $A=\begin{bmatrix}2 & \frac{9}{2}\\\frac{9}{2} & 8\end{bmatrix}$
Help Clay6 to be free
Clay6 needs your help to survive. We have roughly 7 lakh students visiting us monthly. We want to keep our services free and improve with prompt help and advanced solutions by adding more teachers and infrastructure.

A small donation from you will help us reach that goal faster. Talk to your parents, teachers and school and spread the word about clay6. You can pay online or send a cheque.

Thanks for your support.
Continue
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Continue
Clay6 tutors use Telegram* chat app to help students with their questions and doubts.
Do you have the Telegram chat app installed?
Already installed Install now
*Telegram is a chat app like WhatsApp / Facebook Messenger / Skype.
...