Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 6 Subquestion (iii) Maths Textbook Solution.

Answer: $A= \begin{bmatrix} 2 &2 &2 &2\\ 4 &4 &4 &4 \\ 6 &6 &6 &6 \end{bmatrix}$

Given: $a_{ij}= \left (2i \right )$
Here we have to construct $3\times 4$  matrix according to $\left (2i \right )$

Hint: Substitute the required value according $\left (2i \right )$

Solution: Here $a_{ij}= \left (2i \right )$

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

So, $A= \begin{bmatrix} a_{11} &a_{12} &a_{13} & a_{14}\\ a_{21} &a_{22} & a_{23} & a_{24}\\ a_{31} & a_{32} & a_{33} &a_{34} \end{bmatrix}_{3\times 4}$

$\! \! \! \! \! \! \! \! \! a_{11}= 2\times 1= 2\\a_{12}= 2\times 1= 2\\a_{13}= 2\times 1=2\\a_{14}= 2\times 1= 2$             $\! \! \! \! \! \! \! \! \! a_{21}= 2\times 2= 4\\a_{22}= 2\times 2= 4\\a_{23}= 2\times 2=4\\a_{24}= 2\times 2= 4$            $\! \! \! \! \! \! \! \! \! a_{31}= 2\times 3= 6\\a_{32}= 2\times 3= 6\\a_{33}= 2\times 3=6\\a_{34}= 2\times 3= 6$

Substituting these values in Matrix $A$ , we get

$A= \begin{bmatrix} 2 &2 &2 &2\\ 4 &4 &4 &4 \\ 6 &6 &6 &6 \end{bmatrix}$