Linear Algebra with Applications, 10th Edition

3.3

1. 1. (a) and (e) are linearly independent; (b), (c), and (d) are linearly dependent.

2. 2. (a) and (e) are linearly independent; (b), (c), and (d) are not.

3. 3. 

   1. (a) and (b) are all of 3-space;

   2. (c) a plane through $(0,0,0)$;

   3. (d) a line through $(0,0,0)$;

   4. (e) a plane through $(0,0,0)$

4. 4. 

   1. (a) linearly independent;

   2. (b) linearly independent;

   3. (c) linearly dependent

5. 8. (a) and (b) are linearly dependent while (c) and (d) are linearly independent.

6. 11. When $\alpha$ is an odd multiple of $\pi /2$. If the graph of y = cos x is shifted to the left or right by an odd multiple of $\pi /2$, we obtain the graph of either $\text{sin }x\text{ or }-\text{ sin }x$.