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

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

Answers (1)

Answer:   A= \begin{bmatrix} \frac{1}{2} &\frac{9}{2} \\ \0 & 2 \end{bmatrix}

Given:  a_{ij}= \frac{\left ( i-2j \right )^{2}}{2} 
            Here we have to construct 2\times 2   matrix according to \frac{\left ( i-2j \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 ( 1-2\times 1 \right )^{2}}{2}= \frac{-1^{2}}{2}= \frac{1}{2}\\a_{12}= \frac{\left ( 1-2\times 2 \right )^{2}}{2}= \frac{\left ( -3 \right )^{2}}{2}= \frac{9}{2}                    \! \! \! \! \! \! \! \! \! a_{21}= \frac{\left ( 2-1 \times 1\right )^{2}}{2}=\frac{\left ( 0 \right )^{2}}{2} = 0\\a_{22}= \frac{\left ( 2-2 \times 2\right )^{2}}{2}= \frac{ -2 ^{2}}{2}= \frac{4}{2}= 2 
Substituting these values in Matrix A , we get

A= \begin{bmatrix} \frac{1}{2} &\frac{9}{2} \\ \0 & 2 \end{bmatrix}

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