Exercise 3.4.8

Answers

Do the same just like what we’ve done in the previous exercise.

(\begin{matrix} 2 & - 6 & 3 & 2 & - 1 & 0 & 1 & 2 \\ - 3 & 9 & - 2 & - 8 & 1 & - 3 & 0 & - 1 \\ 4 & - 12 & 7 & 2 & 2 & - 18 & - 2 & 1 \\ - 5 & 15 & - 9 & - 2 & 1 & 9 & 3 & - 9 \\ 2 & - 6 & 1 & 6 & - 3 & 12 & - 2 & 7 \end{matrix})

⇝ (\begin{matrix} 1 & - 3 & \frac{3}{2} & 1 & - \frac{1}{2} & 0 & \frac{1}{2} & 1 \\ 0 & 0 & 1 & - 2 & - \frac{1}{5} & - \frac{6}{5} & \frac{3}{5} & \frac{4}{5} \\ 0 & 0 & 0 & 0 & 1 & - 4 & - \frac{23}{21} & - \frac{19}{21} \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & - 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \end{matrix})

We know that ${u_{1}, u_{3}, u_{5}, u_{7}}$ is a basis for $W$ .

jephianlin

2011-06-27 00:00