Construct $a_{2\times 2}$ matrix where $a_{ij} =|2i+3j|$

Answer 1

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

$a_{ij}=|2i+3j|$

Replace i=1,j=1.

$a_{11}=|2(1)+3(1)|$

$\;\;\;\;\;\;=|2+3|$

$\;\;\;\;\;\;=5$

$a_{12}=|2i+3j|$

Replace i=1,j=2.

$a_{12}=|2(1)+3(2)|$

$\;\;\;\;\;\;=|2+6|=|8|=8$

Step 2:

$a_{21}=|2i+3j|$

Replace i=2,j=1.

$a_{21}=|2(2)+3(1)|$

$\;\;\;\;\;\;=|4+3|=|7|=7.$

$a_{22}=|2i+3j|$

Replace i=2,j=2.

$a_{22}=|2(2)+3(2)|$

$\;\;\;\;\;\;=|4+6|=|10|=10.$

Step3:

Hence the required matrix is given by $A=\begin{bmatrix}5 & 8\\7 &10\end{bmatrix}$