## Chapter 9 Exercise B

1. Solution: Choose an orthonormal basis of $\mathbb{R}^3$ that puts the matrix of $S$ in the form given by 9.36. Since $\mathcal{M}(S)$ is a $3$-by-$3$ matrix, one of the diagonal…

1. Solution: Choose an orthonormal basis of $\mathbb{R}^3$ that puts the matrix of $S$ in the form given by 9.36. Since $\mathcal{M}(S)$ is a $3$-by-$3$ matrix, one of the diagonal…

1. Solution: $V_\mathbb{C}$ is clearly closed under addition. We can write each complex number in the form $a + bi$ for some $a, b \in \mathbb{R}$ and we have $$…