Browse Questions

# Construct a 2 x 2 matrix $A = [ a_{ij} ]$, whose elements are given by $a_{ij}$ is $\large\frac{( \hat i + \hat j )^2}{2}$

Toolbox:
• The number or functions occurring in the rectangular array are called the elements of the matrix or entries of the matrix. The element of the matrix is given by ith row and jth column.
• 2 x 2 matrix = $A=\begin{bmatrix}a{11} & a{12}\\a{21} & a{22}\end{bmatrix}$
Step1:
Given:
$a_{ij}=\frac{(i+j)^2}{2}$
$a_{11}$ where i=1,j=1
$a_{11}=\frac{(1+1)^2}{2}=\frac{2^2}{2}=\frac{4}{2}=2.$
$a_{12}$ where i=1,j=2
$a_{11}=\frac{(1+2)^2}{2}=\frac{3^2}{2}=\frac{9}{2}.$
Step 2:
$a_{21}$ where i=2,j=1
$a_{21}=\frac{(2+1)^2}{2}=\frac{3^2}{2}=\frac{9}{2}.$
$a_{22}$ where i=2,j=2
$a_{22}=\frac{(2+2)^2}{2}=\frac{4^2}{2}=\frac{16}{2}=8.$
Step3:
Hence $A=\begin{bmatrix}2 & \frac{9}{2}\\\frac{9}{2} & 8\end{bmatrix}$