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  • Provide solution for RD Sharma maths class 12 chapter 4 Algebra of Matrices exercise Fill in the blank question 18

Provide solution for RD Sharma maths class 12 chapter 4 Algebra of Matrices exercise Fill in the blank question 18

Answers (1)

Answer:

 z = x + y

Hint:

 Use the basic of matrix.

Given:

 F(x) F(y) = F(z)

Solution:

\begin{aligned} &F(x) F(y)=\left[\begin{array}{cc} \cos x & \sin x \\ -\sin x & \cos x \end{array}\right]\left[\begin{array}{cc} \cos y & \sin y \\ -\sin y & \cos y \end{array}\right] \\ &=\left[\begin{array}{cc} \cos x \cos y+(-\sin x \sin y) & -\cos x \sin y-\sin x \cos y \\ \cos y \sin x+\cos x \sin y & -\sin x \sin y+\cos x \cos y \end{array}\right] \\ &=\left[\begin{array}{cc} \cos (x+y) & -\sin (x+y) \\ \sin (x+y) & \cos (x+y) \end{array}\right] \end{aligned}

So,

 F(x) F(y) = F(z) = F(x + y)

Hence,

 z = x + y

Posted by

Gurleen Kaur

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