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

Answer: $A= \begin{bmatrix} 1 &\frac{1}{2} \\ \\ \frac{5}{2} & 2 \end{bmatrix}$

Given:  $a_{ij}= \frac{\left |-3i+j \right |}{2}$
Here we have to construct $2\times 2$  matrix according to  $a_{ij}= \frac{\left |-3i+j \right |}{2}$

Hint:    Substitute required values in the $2\times 2$  matrix

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

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

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

$\! \! \! \! \! \! \! \! \! a_{11}= \frac{\left | -3\times 1+1 \right |}{2}= \frac{2}{2}= 1\\ \\a_{12}= \frac{ \left |-3\times 1+ 2 \right |}{2}= \frac{ 1 }{2}$                  $\! \! \! \! \! \! \! \! \! a_{21}= \frac{ \left | -3\times 2+1 \right |}{2}=\frac{5 }{2}\\ \\a_{22}= \frac{\left | -3\times 2+2 \right | }{2}= \frac{ 4}{2}= 2$

Substituting these values in Matrix $A$ , we get

$A= \begin{bmatrix} 1 &\frac{1}{2} \\ \\ \frac{5}{2} & 2 \end{bmatrix}$