Exercise 3.4.9

Answers

Use the representation of those matrix with some basis (usually take the standard basis) and do the same thing like previous questions on them.

(\begin{matrix} 0 & 1 & 2 & 1 & - 1 \\ - 1 & 2 & 1 & - 2 & 2 \\ - 1 & 2 & 1 & - 2 & 2 \\ 1 & 3 & 9 & 4 & - 1 \end{matrix})

⇝ (\begin{matrix} 1 & - 2 & - 1 & 2 & - 2 \\ 0 & 1 & 2 & 1 & - 1 \\ 0 & 0 & 0 & 1 & - 2 \\ 0 & 0 & 0 & 0 & 0 \end{matrix})

So we know that the subset containing the first, the second, and the fourth matrix forms a basis for $W$ .

jephianlin

2011-06-27 00:00