ELLIPSES - ECONOMETRIC THEORY: Exercise 2 Matrix...

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ECONOMETRIC THEORY: Exercise 2 Matrix Multiplication: Orthonormal Matrices and Rotations. 1. Find following matrix product: S 1 0 0 S 2 ‚• 1 ρ ρ 1 S 1 0 0 S 2 . 2. Confirm that, if θ =45 , then cos θ - sin θ sin θ cos θ = " 1 2 - 1 2 1 2 1 2 # . 3. Use the definitions of a sine and a cosine together with Pythagorus theorem to prove that sin 2 + cos 2 =1. 4. Confirm that cos θ sin θ - sin θ cos θ cos θ - sin θ sin θ cos θ = 10 01 and that cos θ - sin θ sin θ cos θ cos θ sin θ - sin θ cos θ = . 5. Calculate the product " 1 2 1 2 - 1 2 1 2 # 1 - ρ 0 + ρ " 1 2 - 1 2 1 2 1 2 # . 6. Calculate the product
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