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

Answer:   $A= \begin{bmatrix} 0 &-1 &-2 &-3\\ 1 &0 &-1 &-2 \\ 2 &1 &0 &-1 \end{bmatrix}$

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

Hint: Find the sum of $i$ and $j$  for each element.

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

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

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

$\! \! \! \! \! \! \! \! \! a_{11}= 1-1= 0\\a_{12}= 1-2= -1\\a_{13}= 1-3=-2\\a_{14}= 1-4= -3$             $\! \! \! \! \! \! \! \! \! a_{21}= 2-1= 1\\a_{22}= 2-2= 0\\a_{23}= 2-3=-1\\a_{24}= 2-4= -2$           $\! \! \! \! \! \! \! \! \! a_{31}= 3-1= 2\\a_{32}= 3-2= 1\\a_{33}= 3-3=0\\a_{34}= 3-4= -1$

Substituting these values in Matrix $A$ , we get

$A= \begin{bmatrix} 0 &-1 &-2 &-3\\ 1 &0 &-1 &-2 \\ 2 &1 &0 &-1 \end{bmatrix}$