#### Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 5 Suquestion (v) Maths Textbook Solution.

Answer:  $A= \begin{bmatrix} \frac{1}{2} &2 \\ \\ \frac{1}{2} & 1 \end{bmatrix}$

Given:  $a_{ij}= \frac{\left | 2 i-3j \right |}{2}$
Here we have to construct $2\times 2$  matrix according to   $\frac{\left | 2 i-3j \right |}{2}$
Hint:  Substitute required values in the $2\times 2$  matrix according $\frac{\left | 2 i-3j \right |}{2}$

Solution:  Let   $A= \left [ a_{ij} \right ]_{2\times 2}$

So, the elements in a $2\times 2$  are $a_{11},a_{12},a_{21},a_{22}$

$A= \begin{bmatrix} a_{11} &a_{12} \\ a_{21} & a_{22} \end{bmatrix}$

$\! \! \! \! \! \! \! \! \! a_{11}= \frac{\left | 2\times 1-3\times 1 \right |}{2}= \frac{1}{2}\\ \\a_{12}= \frac{ \left |2\times 1-3\times 2 \right |}{2}= \frac{ 4 }{2}= 2$                      $\! \! \! \! \! \! \! \! \! a_{21}= \frac{ \left | 2\times 2-3\times 1 \right |}{2}=\frac{4-3 }{2} = \frac{1}{2}\\ \\a_{22}= \frac{\left | 2\times 2-3\times 2 \right | }{2}= \frac{ 2}{2}= 1$

Substituting these values in Matrix $A$ , we get

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