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

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

Answers (1)

Answer: A= \begin{bmatrix} 0 &\frac{1}{2} \\ \frac{1}{2} & 0 \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}= 0\\a_{12}= \frac{\left ( 1-2 \right )^{2}}{2}= \frac{\left ( 1 \right )^{2}}{2}= \frac{1}{2}                              \! \! \! \! \! \! \! \! \! a_{21}= \frac{\left ( 2-1 \right )^{2}}{2}=\frac{1 }{2}\\a_{22}= \frac{\left ( 2-2 \right )^{2}}{2}=0

Substituting these values in Matrix A , we get

A= \begin{bmatrix} 0 &\frac{1}{2} \\ \frac{1}{2} & 0 \end{bmatrix}

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