Exercise 4.2.1

Answers

1.: No. See Exercise 4.1.1(a).
2.: Yes. This is Theorem 4.4.
3.: Yes. This is the Corollary after Theorem 4.4.
4.: Yes. This is Theorem 4.5.
5.: No. For example, the determinant of $(\begin{matrix} 2 & 0 \\ 0 & 1 \end{matrix})$ is $2$ but not $\det (I) = 1$ .
6.: No. We have that $(\begin{matrix} 1 & 0 \\ 2 & 1 \end{matrix}) = 1 \neq 2 \det (I) = 2$ .
7.: No. For example, the determinant of identity matrix is $1$ .
8.: Yes. See Exercise 4.2.23.

jephianlin

2011-06-27 00:00