Vectors

Step 1: Define linear operators. Linear operators satisfy two properties for any vectors and scalar : (additivity) (scalar multiplication)

Step 2: Analyze each option. : This is correct because the addition of two linear operators applied to distributes over the addition. : This is correct because scalar multiplication of a linear operator applies directly to the result of . : This is correct because the composition of two linear operators and acting on satisfies this property. : This is incorrect because the transpose ( ) is not involved unless explicitly stated, and it does not apply to the given scenario.