logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  CBSE XII  >>  Math  >>  Matrices
0 votes

Construct $a_{2\times 2}$ matrix where $a_{ij} =\frac{(i + 2j)^2}{2}$

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • In general $a_{2\times 2}$ matrix is given by $A=\begin{bmatrix}a_{11} & a_{12}\\a_{21} &a_{22}\end{bmatrix}$
Step1:
Elements are given by
$a_{ij}=\frac{(i+2j)^2}{2}$
Replace i=1,j=1.
$a_{11}=\frac{(1+2(1))^2}{2}$
$\;\;\;=\frac{(1+2)^2}{2}=\frac{3^2}{2}=9/2.$
$a_{12}=\frac{(1+2(2))^2}{2}$
Replace i=1,j=2.
$\;\;\;=\frac{(1+4)^2}{2}=\frac{5^2}{2}=25/2.$
Step2
$a_{21}=\frac{(2+2(1))^2}{2}$
Replace i=2,j=1.
$\;\;\;=\frac{(2+2)^2}{2}=\frac{4^2}{2}=16/2=8$
$a_{22}=\frac{(2+2(2))^2}{2}$
Replace i=2,j=2.
$\;\;\;=\frac{(2+4)^2}{2}=\frac{6^2}{2}=36/2=18$
Step3:
Hence the required matrix is given by\[A=\begin{bmatrix}9/2 & 25/2\\8 &18\end{bmatrix}\]
answered Mar 21, 2013 by sharmaaparna1
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...