If A = [[cos θ, -sin θ], [sin θ, cos θ]], then the matrix A⁻⁵⁰ when θ = π/12, is equal to:

Question

Accepted Answer

[[√3/2, 1/2], [-1/2, √3/2]]. A is a rotation matrix, so A^n rotates by n*theta. With theta=pi/12, -50*theta = -25pi/6 = -pi/6 (mod 2pi). Thus A^(-50) = [[cos(-pi/6), -sin(-pi/6)],[sin(-pi/6), cos(-pi/6)]] = [[sqrt(3)/2, 1/2],[-1/2, sqrt(3)/2]].

If A = [[cos θ, -sin θ], [sin θ, cos θ]], then the matrix A⁻⁵⁰ when θ = π/12, is equal to:

Solution

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