Exercise 1.5.2

Answers

1.: Linearly dependent. We have $- 2 (\begin{matrix} 1 & - 3 \\ - 2 & 4 \end{matrix}) = (\begin{matrix} - 2 & 6 \\ 4 & - 8 \end{matrix})$ . So to check the linearly dependency is to find the nontrivial solution of equation $a_{1} x_{1} + a_{2} x_{2} + \dots + a_{n} x_{n} = 0$ . And $x_{1}$ and $x_{2}$ are the two matrices here.
2.: Linearly independent.
3.: Linearly independent.
4.: Linearly dependent.
5.: Linearly dependent.
6.: Linearly independent.
7.: Linearly dependent.
8.: Linearly independent.
9.: Linearly independent.
10.: Linearly dependent.

jephianlin

2011-06-27 00:00