Tamil Nadu Board of Secondary EducationHSC Arts Class 11th

# Consider the matrix Aα = [cosα-sinαsinαcosα] Show that AAAAαAβ=A(α+β) - Mathematics

Sum

Consider the matrix Aα = [(cos alpha, - sin alpha),(sin alpha, cos alpha)] Show that "A"_alpha "A"_beta = "A"_((alpha + beta))

#### Solution

"A"_alpha "A"_beta = [(cos alpha, - sin alpha),(sin alpha, cos alpha)] [(cos beta, - sin beta),(sin beta, cos beta)]

= [(cos alpha cos beta - sin alpha sin beta, - cos alpha sin beta - sin alpha cos beta),(sin alpha cos beta + cos alpha sin beta, - sin alpha sin beta + cos alpha cos beta)]

= [(cos alpha cos beta - sin alpha sin beta, -(sinalpha cos beta + cos alpha sin beta)),(sin alpha cos beta + cos alpha sin beta, cos alpha cos beta - sin alpha sin beta)]

"A"_alpha "A"_beta = [(cos(alpha + beta), - sin(alpha + beta)),(sin(alpha + beta) , cos(alpha + beta))]

From equation (1), (2) and (3)

"A"_alpha "A"_beta = "A"_((alpha + beta))

Concept: Matrices
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#### APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 11th Mathematics Volume 1 and 2 Answers Guide
Chapter 7 Matrices and Determinants
Exercise 7.1 | Q 6. (i) | Page 18
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