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

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

Answers (1)

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

Given:  a_{ij}= \frac{\left | 2 i-3j \right |}{2}
            Here we have to construct 2\times 2  matrix according to   \frac{\left | 2 i-3j \right |}{2}
Hint:  Substitute required values in the 2\times 2  matrix according \frac{\left | 2 i-3j \right |}{2}

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 1-3\times 1 \right |}{2}= \frac{1}{2}\\ \\a_{12}= \frac{ \left |2\times 1-3\times 2 \right |}{2}= \frac{ 4 }{2}= 2                      \! \! \! \! \! \! \! \! \! a_{21}= \frac{ \left | 2\times 2-3\times 1 \right |}{2}=\frac{4-3 }{2} = \frac{1}{2}\\ \\a_{22}= \frac{\left | 2\times 2-3\times 2 \right | }{2}= \frac{ 2}{2}= 1

Substituting these values in Matrix A , we get

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

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