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

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

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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}

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