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  • Need solution for RD Sharma maths class 12 chapter 4 Algebra of Matrices exercise Fill in the blank question 15

Need solution for RD Sharma maths class 12 chapter 4 Algebra of Matrices exercise Fill in the blank question 15

Answers (1)

Answer:

 \begin{bmatrix} 1 &0 \\ 0 &1 \end{bmatrix}

Hint:

 Use the basic method of multiplication.

Given:

 A=\left[\begin{array}{cc} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right]

Solution:

Calculate,

A^{T}=\left[\begin{array}{cc} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right]

So,

\begin{aligned} &A \times A^{T}=\left[\begin{array}{cc} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right] \times\left[\begin{array}{cc} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right] \\ &A \times A^{T}=\left[\begin{array}{cc} \cos ^{2} \theta+\sin ^{2} \theta & -\cos \theta \sin \theta+\cos \theta \sin \theta \\ -\sin \theta \cos \theta+\cos \theta \sin \theta & \sin ^{2} \theta+\cos ^{2} \theta \end{array}\right] \\ &A \times A^{T}=\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right] \end{aligned}

 

Posted by

Gurleen Kaur

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