Chapter 53

Chapter 5 Exercise C
1. Solution: It is not said $V$ is finite-dimensional, but I will do it by assuming $\dim V<\inft...
Chapter 5 Exercise B
1. Solution: (a) Note that \[ (I-T)(I+T+\cdots+T^{n-1})=I-T^n=I \]and \[ (I+T+\cdots+T^{n-1})(I-T)=I...
Chapter 5 Exercise A
1. Solution: (a) For any $u\in U$, then $Tu=0\in U$ since $U\subset \m{null} T$, hence $U$ is invari...