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

Answer: $A= \begin{bmatrix} \frac{9}{2} &8 \\ \\ \frac{25}{2} & 18 \end{bmatrix}$

Given: $a_{ij}= \frac{\left ( 2i+j \right )^{2}}{2}$

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

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 $a_{11},a_{12},a_{21},a_{22}$

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

$\! \! \! \! \! \! \! \! \! a_{11}= \frac{\left ( 2\times 1+1 \right )^{2}}{2}= \frac{3^{2}}{2}= \frac{9}{2}\\a_{12}= \frac{\left ( 2\times 1+2 \right )^{2}}{2}= \frac{\left ( 4 \right )^{2}}{2}= \frac{16}{2}= 8$              $\! \! \! \! \! \! \! \! \! a_{21}= \frac{\left ( 2 \times 2+1\right )^{2}}{2}=\frac{\left ( 5 \right )^{2}}{2} = \frac{25}{2}\\a_{22}= \frac{\left ( 2 \times 2+2\right )^{2}}{2}= \frac{ 6 ^{2}}{2}= \frac{36}{2}= 18$

Substituting these values in Matrix $A$ , we get

$A= \begin{bmatrix} \frac{9}{2} &8 \\ \\ \frac{25}{2} & 18 \end{bmatrix}$