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

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Answer:  A= \begin{bmatrix} e^{2x}\sin x &e^{2x}\sin 2x \\ e^{4x} \sin x& e^{4x}\sin 2x \end{bmatrix}

Given:  a_{ij}= e^{2x}\sin xj
            Here we have to construct 2\times 2  matrix according to  e^{2x}\sin xj

Hint:  Putting the value of each row and column element according to the question in matrix

Solution:  Let  A= \left [ a_{ij} \right ]_{2\times 2}  = e^{2x}\sin xj

  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}= e^{2\times 1x}\sin x\times 1= e^{2x}\sin x\\a_{12}= e^{2\times 1x}\sin x\times 2= e^{2x}\sin 2x           \! \! \! \! \! \! \! \! \! a_{21}= e^{2\times 2x}\sin x\times 1= e^{4x}\sin x\\a_{22}= e^{2\times 2x}\sin x\times 2= e^{4x}\sin 2x

Substituting these values in Matrix A , we get

A= \begin{bmatrix} e^{2x}\sin x &e^{2x}\sin 2x \\ e^{4x} \sin x& e^{4x}\sin 2x \end{bmatrix}

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