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Simplify  Cos Theta[(Cos Theta, Sintheta),(-sin Theta, Cos Theta)] + Sin Theta [(Sin Theta, -cos Theta), (Cos Theta, Sin Theta)] - CBSE (Science) Class 12 - Mathematics

ConceptOperations on Matrices Multiplication of a Matrix by a Scalar

Question

Simplify  cos theta[(cos theta, sintheta),(-sin theta, cos theta)] + sin theta [(sin theta, -cos theta), (cos theta, sin theta)]

Solution

cos theta[(cos theta ,sin theta),(-sin theta, cos theta)] + sin theta [(sin theta, -cos theta),(cos theta, sin theta)]

= [(cos^2 theta, cos theta sin theta),(-sin thetacos theta, cos^2 theta)] + [(sin^2 theta, -sin thetacos theta),(sin thetacos theta, sin^2 theta)]

= [(cos^2 theta + sin^2 theta, cos theta sintheta-sin thetacos theta),(-sin thetacos theta+sin theta cos theta, cos^2 theta + sin^2 theta)]

= [(1,0),(0,1)]     (∵ cos^2 theta + sin^2 theta = 1)

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Solution Simplify  Cos Theta[(Cos Theta, Sintheta),(-sin Theta, Cos Theta)] + Sin Theta [(Sin Theta, -cos Theta), (Cos Theta, Sin Theta)] Concept: Operations on Matrices - Multiplication of a Matrix by a Scalar.
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