Exercise 3.1.3

Answers

1.

This matrix interchanges the first and the third row. So the inverse matrix do the inverse step. So the inverse matrix do the same thing and it is

(\begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{matrix}) .

2.

This matrix multiplies the second row by

3

. To the inverse matrix multiplies the second row by

\frac{1}{3}

and it is

(\begin{matrix} 1 & 0 & 0 \\ 0 & \frac{1}{3} & 0 \\ 0 & 0 & 1 \end{matrix}) .

3.

This matrix adds

- 2

times the first row to the third row. So the invers matrix adds

2

times the first row to the third row and it is

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

jephianlin

2011-06-27 00:00