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

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 $A=\begin{bmatrix}5 & 8\\7 &10\end{bmatrix}$
answered Mar 21, 2013
edited Apr 3, 2013