Ex 3.3, 12 (MCQ) - Chapter 3 Class 12 Matrices
Last updated at April 16, 2024 by Teachoo
Transpose of a matrix
Last updated at April 16, 2024 by Teachoo
Ex 3.3, 12 If A = [β 8(cos πΌ&γβsinγβ‘πΌ@sinβ‘πΌ&cosβ‘πΌ )] , then A + Aβ = I , if the value of Ξ± is A. π/π B. π/π C. Ο D. ππ/π A = [β 8(cosβ‘πΌ&γβsinγβ‘πΌ@sinβ‘πΌ&cosβ‘πΌ )] Aβ= [β 8(cosβ‘πΌ&sinβ‘πΌ@γβsinγβ‘πΌ&cosβ‘πΌ )] and I = [β 8(1&0@0&1)] Given A + Aβ = I [β 8(ππ¨π¬β‘πΆ&γβπ¬π’π§γβ‘πΆ@π¬π’π§β‘πΆ&ππ¨π¬β‘πΆ )] + [β 8(ππ¨π¬β‘πΆ&π¬π’π§β‘πΆ@γβπ¬π’π§γβ‘πΆ&ππ¨π¬β‘πΆ )] = [β 8(π&π@π&π)] [β 8(cosβ‘γπΌ+cosβ‘πΌ γ&γβsinγβ‘γπΌ+sinβ‘πΌ γ@sinβ‘πΌ γβsinγβ‘πΌ&cosβ‘γπΌ+cosβ‘πΌ γ )]= [β 8(1&0@0&1)] [β 8(πππ¨π¬β‘πΆ&π@π&πππ¨π¬β‘πΆ )]= [β 8(π&π@π&π)] Since the matrices are equal, corresponding elements are equal 2cos πΆ = 1 cosβ‘πΌ = 1/2 cosβ‘πΌ = cosβ‘γ60Β°γ Comparing angles πΌ = 60Β° πΌ = 60Β° Γ π/(180Β°) πΆ = π /π So the correct answer is (B)