Question

$\huge{\green}\fcolorbox{red}{b}{\underline{\color{purple}{Qᴜᴇsᴛɪᴏɴ}}}$


Construct a 2 × 2 matrix whose elements aᵢⱼ are given by aᵢⱼ = i + j.​

Answer 1

$\large\underline{\sf{Solution-}}$

Let us consider a matrix of order 2 × 2, as

$\begin{gathered}\sf \rm :\longmapsto\:\:A=\left[\begin{array}{cc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right]\end{gathered}$

Now, it is given that

$\bf :\longmapsto\:a_{ij} = i + j$

Thus,

$\bf :\longmapsto\:a_{11} = 1 + 1 = 2$

$\bf :\longmapsto\:a_{12} = 1 + 2 = 3$

$\bf :\longmapsto\:a_{21} = 2 + 1= 3$

$\bf :\longmapsto\:a_{22} = 2 + 2= 4$

So, on substituting all these values in above matrix, we get

$\begin{gathered}\sf \bf :\longmapsto\:\:A=\left[\begin{array}{cc}2&3\\3&4\end{array}\right]\end{gathered}$

Additional Information :-

Let us consider a matrix A of order m × n, then order of matrix represents following information :

1. Number of elements in given matrix = mn

2. Number of elements in each row = n

3. Number of elements in each column = m.

Answer 2

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Let us consider a matrix of order 2 × 2, as

$\begin{gathered}\begin{gathered}\sf \rm :\longmapsto\:\:A=\left[\begin{array}{cc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right]\end{gathered}\end{gathered} </p><p>:⟼A=[ </p><p>a </p><p>11</p><p> </p><p> </p><p>a </p><p>21</p><p> </p><p> </p><p> </p><p> </p><p>a </p><p>12</p><p> </p><p> </p><p>a </p><p>22</p><p> </p><p> </p><p> </p><p> ]$

Now, it is given that

$\bf :\longmapsto\:a_{ij} = i + j:⟼a </p><p>ij</p><p> </p><p> =i+j</p><p></p><p>Thus,</p><p></p><p>\bf :\longmapsto\:a_{11} = 1 + 1 = 2:⟼a </p><p>11</p><p> </p><p> =1+1=2</p><p></p><p>\bf :\longmapsto\:a_{12} = 1 + 2 = 3:⟼a </p><p>12</p><p> </p><p> =1+2=3</p><p></p><p>\bf :\longmapsto\:a_{21} = 2 + 1= 3:⟼a </p><p>21</p><p> </p><p> =2+1=3</p><p></p><p>\bf :\longmapsto\:a_{22} = 2 + 2= 4:⟼a </p><p>22$

=2+2=4

So, on substituting all these values in above matrix, we get

$\begin{gathered}\begin{gathered}\sf \bf :\longmapsto\:\:A=\left[\begin{array}{cc}2&3\\3&4\end{array}\right]\end{gathered}\end{gathered} </p><p>:⟼A=[ 23 / 34 ]$

Additional Information :-

Let us consider a matrix A of order m × n, then order of matrix represents following information :

1. Number of elements in given matrix = mn

2. Number of elements in each row = n

3. Number of elements in each column = m.