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

Answer:    $A= \begin{bmatrix} 2 &\frac{9}{2} \\ \frac{9}{2} & 8 \end{bmatrix}$

Given:   $\frac{\left ( i+j \right )^{2}}{2}$
Here we have to construct $2\times 2$  matrix according to   $\frac{\left ( i+j \right )^{2}}{2}$

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  $a_{11},a_{12},a_{21},a_{22}$

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

$\! \! \! \! \! \! \! \! \! a_{11}= \frac{\left ( 1+1 \right )^{2}}{2}= \frac{4}{2}= 2\\a_{12}= \frac{\left ( 1+2 \right )^{2}}{2}= \frac{\left ( 3 \right )^{2}}{2}= \frac{9}{2}= 4.5$                  $\! \! \! \! \! \! \! \! \! a_{21}= \frac{\left ( 2+1 \right )^{2}}{2}=\frac{\left ( 3 \right )^{2}}{2} = \frac{9}{2}= 4.5\\a_{22}= \frac{\left ( 2+2 \right )^{2}}{2}= \frac{\left ( 4 \right )^{2}}{2}= \frac{16}{2}= 8$
Substituting these values in Matrix $A$ , we get

$A= \begin{bmatrix} 2 &\frac{9}{2} \\ \frac{9}{2} & 8 \end{bmatrix}$