Exercise 2.4.2

Answers

1.: No. They have different dimension $2$ and $3$ .
2.: No. They have different dimension $2$ and $3$ .
3.: Yes. $T^{- 1} (a_{1}, a_{2}, a_{3}) = (- \frac{4}{3} a_{2} + \frac{1}{3} a_{3}, a_{2}, - \frac{1}{2} a_{1} - 2 a_{2} + \frac{1}{2} a_{3})$ .
4.: No. They have different dimension $4$ and $3$ .
5.: No. They have different dimension $4$ and $3$ .
6.: Yes. $T^{- 1} (\begin{matrix} a & b \\ c & d \end{matrix}) = (\begin{matrix} b & a - b \\ c & d - c \end{matrix})$ .

jephianlin

2011-06-27 00:00