Question

Construct a 2 X 2 Matrix Whose Elements Aij Are Given by Aij = 2i - J​

Answer 1

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

Let consider the matrix of 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 elements of matrix A is given by

$\red{\rm :\longmapsto\:a_{ij} = 2i - j}$

Now, Lets evaluate the elements of matrix A,

$\red{\rm :\longmapsto\:a_{11} = 2 \times 1 - 1 = 2 - 1 = 1}$

$\red{\rm :\longmapsto\:a_{12} = 2 \times 1 - 2 = 2 - 2 = 0}$

$\red{\rm :\longmapsto\:a_{21} = 2 \times 2 - 1 = 4 - 1 = 3}$

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

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

$\begin{gathered}\sf \rm :\longmapsto\:\:A=\left[\begin{array}{cc}1&0\\3&2\end{array}\right]\end{gathered}$

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.