Question

solve this fast ... it's urgent ... don't give any irrelevant ansr ​

Answer 1

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

Let us consider a 2 × 2 matrix as

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

According to given,

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

So,

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

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

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

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

So, required matrix is

$\red{\rm :\longmapsto\:A=\bigg[ \begin{matrix}1&0 \\ 3&2 \end{matrix} \bigg]}$

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

Let us consider a 2 × 2 matrix as

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

According to given,

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

So,

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

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

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

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

So, required matrix is

$\red{\rm :\longmapsto\:A=\bigg[ \begin{matrix}1&2 \\ 2&4 \end{matrix} \bigg]}$

Additional Information :-

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

1. Number of elements in matrix.

2. Number of elements in each row( = number of columns)

3. Number of elements in each column ( = number of rows)