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Chapter 8 Exercise D

1. Solution: By Exercise 11 in section 8B the characteristic polynomial is $z^4$ and by 8.46 this is a polynomial multiple of the minimal polynomial. Since $N^3 \neq 0$, it…

Chapter 7 Exercise D

1. Solution. A quick calculation shows that $T^*Tv = ||x||^2\langle v, u \rangle u$ for every $v \in V$. The map $R \in \mathcal{L}(V)$ defined by  Rv = \frac{||x||}{||u||}\langle…

Chapter 3 Exercise D

1. Solution: See Linear Algebra Done Right Solution Manual Chapter 3 Problem 22. It is almost the same. 2. Solution: See Linear Algebra Done Right Solution Manual Chapter 3 Problem…