If A = c o s θ - s i n θ s i n θ c o s θ , then the matrix A - 50 when θ = π 12 , is equal to:

Question

If A = c o s θ - s i n θ s i n θ c o s θ , then the matrix A - 50 when θ = π 12 , is equal to:, 3 2 1 2 - 1 2 3 2, 1 2 3 2 - 3 2 1 2, 3 2 - 1 2 1 2 3 2, 1 2 - 3 2 3 2 1 2

MARKS App · Accepted Answer

A = c o s θ - s i n θ s i n θ c o s θ ⇒ A = c o s θ - s i n θ s i n θ c o s θ = c o s 2 θ + s i n 2 θ = 1 And a d j A = c o s θ s i n θ - s i n θ c o s θ ⇒ A - 1 = 1 A a d j A = c o s θ s i n θ - s i n θ c o s θ ⇒ A - 2 = A - 1 2 = A - 1 A - 1 = c o s θ s i n θ - s i n θ c o s θ c o s θ s i n θ - s i n θ c o s θ = c o s 2 θ - s i n 2 θ 2 s i n θ c o s θ - 2 s i n θ c o s θ c o s 2 θ - s i n 2 θ = c o s 2 θ s i n 2 θ - s i n 2 θ c o s 2 θ It is visible that A - 1 n = c o s n θ s i n n θ - s i n n θ c o s n θ ⇒ A - 50 = A - 1 50 = c o s 50 θ s i n 50 θ - s i n 50 θ c o s 50 θ Now at θ = π 12 , s i n 50 θ = s i n 50 π 12 = s i n π 6 = 1 2 c o s 50 θ = c o s π 6 = 3 2 ⇒ A - 50 = 3 2 1 2 - 1 2 3 2

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