Problem 1 Let VS₁ S₂. Define linear operators P1, P2 on V by P1(81 +82) 81, P2(81 +82) = 82. = These are referred to as projection operators. Show that 1. P = P1, P² = P₂ 2. p₁ + P₂ = I, where I is the identity map on V. 3. P₁0 P2 = P20 P₁ = 0, where 0 os the zero map. 4 V (Ima) (Ima)

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