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

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

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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}

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