T/F

Let H, P e Rnxn be defined by H = 1 - 2uuand P= I - uu". where u e R such that ||u||2 = 1. Determine whether each of the following equations is true or false. 1. Select ] Hz=z, for any vector Z ER" 2. [Select] paz =z, for any vector z ER" 3. [Select] HPz Pz for any vector z e Rn. 4. [Select) PHz = Hz, for any vector z ER" Suggestion. All these questions can be determined algebraically, but it is tedious. Instead, use geometry behind the matrices defined. (Hint. Think in terms of projection and reflection.)