Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 7 Subquestion (iii) Maths Textbook Solution.

$A= \begin{bmatrix} 1 &1 &1\\ 2 &2 & 2\\ 3 & 3 &3\\ 4& 4 & 4 \end{bmatrix}$

Given:  $a_{ij}= i$

Here we have to construct $4\times 3$  matrix according to  $a_{ij}= i$

Hint: First we will find all the elements of matrix according to  $a_{ij}= i$

Solution: Here  $a_{ij}= i$

Let  $A= \left [ a_{ij} \right ]_{4\times 3}$

So, The elements in a $4\times 3$  matrix are $a_{11},a_{21},a_{31},a_{41},a_{12},a_{22},a_{32},a_{42},a_{13},a_{23},a_{33},a_{43}$

$A= \begin{bmatrix} a_{11} & a_{12} &a_{13} \\ a_{21} &a_{22} &a_{23} \\ a_{31} &a_{32} &a_{33} \\ a_{41} & a_{42} & a_{43} \end{bmatrix}_{4\times 3}$

$\! \! \! \! \! \! \! \! \! a_{11}= 1 \\a_{12}=1 \\a_{13}=1$            $\! \! \! \! \! \! \! \! \! a_{21}=2 \\a_{22}=2\\a_{23}=2$          $\! \! \! \! \! \! \! \! \! a_{31}=3\\a_{32}=3\\a_{33}=3$            $\! \! \! \! \! \! \! \! \! a_{41}=4\\a_{42}=4\\a_{43}=4$

Substituting these values in Matrix $A$ , we get

$A= \begin{bmatrix} 1 &1 &1\\ 2 &2 & 2\\ 3 & 3 &3\\ 4& 4 & 4 \end{bmatrix}$