Question

3. Construct a 2 x 2 matrix whose elements a, are given by (i) aij = i.j​

Answer 1

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

Let consider a 2 × 2 matrix 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,

$\red{\rm :\longmapsto\:a_{ij} = i \: .\: j}$

So, let evaluate the elements of matrix A.

$\rm :\longmapsto\:a_{11} = 1 \times 1 = 1$

$\rm :\longmapsto\:a_{12} = 1 \times 2 = 2$

$\rm :\longmapsto\:a_{21} = 2 \times 1 = 2$

$\rm :\longmapsto\:a_{22} = 2 \times 2 = 4$

So, on substituting all these values, in

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

we get

$\begin{gathered}\sf \rm :\longmapsto\:\:A=\left[\begin{array}{cc}1&2 \\2&4\end{array}\right]\end{gathered}$

Additional Information :-

Order of a matrix :- Order of matrix is defined as number of rows × number of columns. Order provides the following information :-

1. Number of elements in a matrix.

2. Number of elements in each row.

3. Number of elements in each column.